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abannavongBest ResponseYou've already chosen the best response.0
i will post the assignment soon!
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
the circled questions btw
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
for the first one, its just 8 thats posted?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
its numbers 10, 14, 16, 18, 22
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
oh i was looking at the first one
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
oh man, that second one's really hard to read lol so lets do the first one
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
k so for 8 what is x approaching? i cant see
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
we dont have to do number 8 lol
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
:\ it looked circled to me lol
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
its only numbers 10, 14, 16, 18, 22
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
do you not have to do the problem in your first attachment?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh yeah duh i forgot i do lolz
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
haha ok cool well i basically cant read any of them cuz they're blurry so can you just type out one that you need help with?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
number 8 its as x goes to infinity
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so it's as x> infinity of (2x^2)/(x^2 +3) ? is that right?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
have y'all talked about L'Hospital's Rule yet?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
what is the L'hospitals rule? can u plz explain
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
i don't think you're supposed to use it if you haven't covered it yet. you don't need it anyway.
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so you start by considering the terms with the highest exponents
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
if I remember correctly, since x is approaching infinity and it's a rational function, you can rewrite it only including the x's with the greatest exponents
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so what would you have if you did that?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
hang on im kinda confused
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
that's ok. so what i'm saying is your next step is to rewrite the limit excluding the +3 in the denominator
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
to exclude the +3 in the denominator how do u do tht?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
you can do this because when x goes to infinity, 2x^5 and x^5 approach infinity and the 3 basically doesn't change the fraction anymore
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
because if you imagine really high numbers, say x=100, x^5 would be 10000000000 and 2x^5 would be 20000000000 and the +3 in the denominator makes less and less of a difference in the fraction. (10000000000/20000000003 is really close to 10000000000/20000000000)
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
in other words, the fraction approaches 1/2
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
im sorry, it approaches 2
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
because 2x^5 is in the numerator
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok so ur limit is basically 2 then right?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok now i get number 8
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so in questions like that, where x is approaching infinity, you can disregard any terms that arent the variables with the highest exponent. like if you had an x^4 being added/subtracted somewhere in the fraction, you could disregard that, too.
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
for the same reason, because as x approaches infinity, they change the fraction less and less, even though it has x in it....those terms approach infinity slower than terms of higher powers.
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
im kinda confused on tht part
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
it's kind of counterintuitive at first
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
as x gets greater, the difference between x^5 and x^4 also gets greater. if x is 10, then x^5 is 100000 and x^4 is 10000, x^5 is 10 times greater than x^4. but when x= 100, x^5 becomes 100 times bigger than x^4, and so on, until x^5 is infinitely bigger than x^4 and you can disregard x^4.
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
can u help me with the continuity limits and onesided ones those ones are the ones that r confusing
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
i can help w one more then i need to get my own work done haha
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so i guess pick one for us to do
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
i think i get the rest on my THQ but i need help with the continuity ones
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
let me post the problem
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow 4} \frac{ \sqrt{x}2 }{ x4 } \]
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so first notice that when x = 4, f(x) = 0/0, which is undefined.
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
and since x is approaching 4 from the left (less than 4, getting greater) both the numerator and denominator are going to be negative...do u get that?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
can u explain it a bit more im still a bit confused
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
sure. so the way i think of it, is to basically imagine x as some number a little less than 4.. 3.something. when you plug that number into the denominator, 3.something  4 is always going to be negative. (anything less than 4)  4 will be negative, right? (34=1, 3.54=0.5, 3.994 = 0.01)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh yeah so its like it keeps on approaching 4 right?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
and for the numerator, you can imagine that since the square root of 4 is 2, the square root of anything less than 4 will be less than 2... when you subtract 2 from that number, the result is negative
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
ya it keeps approaching 4
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
but from the lessthan4 side because it has the minus sign (x>4)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
basically the limit for it will negative right?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
well the numerator and denominator are both negative, right?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so the fraction comes out positive
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
why r limits soo confusing :3
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
lol i know. wanna see my limit problem that no one will answer?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
Limit as x>(pi/2) of [tanx+1/(xpi/2)]?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
thats my question that no one will answer :(
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
i had it on a quiz today
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
can u do the substitution method for tht one
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
no because tan of pi/2 is undefined, it goes to neg infinity and infinity from the right and left....
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh yeah ur right oops lol
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
but im still kinda confused on the continuity limits and onesided ones
 one year ago

nj1202Best ResponseYou've already chosen the best response.0
oh boy satellite's here.... it's about to get real xD
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
i just realized that your problem is tricky. you need to factor your x4 into (sqrt(x)2)(sqrt(x)+2) then cancel out the numerator
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[\lim_{ x\to\frac{\pi}{2}}\frac{\tan(x)+1}{x\frac{\pi}{2}}\]?
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
oooh well that's my problem but not hers
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
somewhere down the list!
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
@jldstuff393 how do u do my problem kinda confuzzled
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
i know i know. u remember difference of squares? like (x^2  4) = (x2)(x+2)?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
is this the problem \[\lim_{x \rightarrow 4} \frac{ \sqrt{x}2 }{ x4 }\]?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh yeah i remember different of squares
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
yeah @satellite73 thts my problem
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
so unless satellite has a less tricky way to solve it, you can factor (x4) as a difference of squares... (sqrt(x)2)(sqrt(x)+2)
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
does that make sense?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
the gimmick here is to "rationalize the numerator" by multiplying by the conjugate of \(\sqrt{x}2\) which is \(\sqrt{x}+2\)
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
cuz when u have that, you can cancel out the (sqrt(x)2) in the numerator and denominator
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
so u multpily the top and bottom by \[\sqrt{x} +2 \]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
this works because \((a+b)(ab)=a^2b^2\) and so \((\sqrt{x}2)(\sqrt{x}+2)=x4\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
that cancels with the \(x4\) in the denominator, which is what you want, you want to cancel the zero
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
and x4 can cancel in denominator
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
so ur limit is one right?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
leaves you with \[\lim_{x \rightarrow 4} \frac{ \sqrt{x}2 }{ x4 }=\lim_{x \rightarrow 4} \frac{1 }{ \sqrt{x}+2}\]\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
no limit is not one, now you have to replace \(x\) by 4
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
once u replace x with 4 u get 1/ 4 right?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
whenever you get \(\frac{0}{0}\) you need some gimmick to factor and cancel to get rid of the zeros
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
satellite would you mind helping me after you're done here? O.o good luck guys!
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
sometime sit is easy sometimes it is a pain. but you get used to it
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
@satellite73 i have some more questions!
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
@jldstuff393 sure if i can what is the question
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
@abannavong go ahead and post them, i will look
 one year ago

jldstuff393Best ResponseYou've already chosen the best response.2
i'll repost it, thanks!
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
kk! thanks @satellite73
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i can't really read it, but for 16 replace \(x\) by 2 in both formulas if you get the same number, that is the limit if you get different numbers, there is no limit
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
number 14 its as deltax goes to 0 with the little plus sign
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
i can't read 18 either is it \(\lim_{ x\to 1^+}\) or \(\lim_{x\to 1^}\)?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
then replace \(x\) by 1 in the second formula you get \(11=0\)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
can u help with 14 also
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
sure, but i can't really read it can you post in a new question? you do not need to write \(\Delta x\) you can just write \(h\) instead
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
it is actually very straight forward we will do a little algebra and that is all
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
kk hang on dinner quickly
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[(x+h)^2+x+h(x^2+x)=x^2+2xh+h^2+x+hx^2x\] \[\cancel{x^2}+2xh+h^2+\cancel{x}+h\cancel{x^2}\cancel{x}=2xh+h+h^2\] divide by \(h\) and get \(2x+1+h\) let \(h\to 0\) be replacing \(h\) by 0 and you get \(2x+1\)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok! @satellite73 im back from dinner
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
that was a quick meal, you should take your time i wrote the solution above, but i used \(h\) instead of \(\Delta x\) it is mostly just algebra, to get rid of the factor of \(\Delta x\) in the denominator, then you replace it by 0
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
im eating and doing work lolz
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you are either eating late or are on the left coast
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
im on the west coast lolz
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
after you finish eating, read my solution above i hope all the steps are clear they are almost all algebra steps, only at the end do you replace \(h\) by 0
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok its jst basic algebra right? so u foil the (x+h)^2 right?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yes exactly it is \((x+h)(x+h)=x^2+2xh+h^2\)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok and then from there u can combine the like terms and get 2xh+h+h^2
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
that is all in the numerator you get \[\frac{2xh+h+h^2}{h}\]
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
and then can u factor out the h on the numerator
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yes factor and cancel or divide each term by \(h\) it is the same thing
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok and then u get 2x+1
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok! i get tht now
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
whew that was exhausting
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow2 ^{+}}(2x\left[ \left x \right \right]\] help im confused with this one also
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
is that an absolute value sign?
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
or is that the floor function?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
its like a bracket and then two straight lines inside
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
do you know what that function is called?
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
ughhh i dont remember what it was called
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
it is either called "floor" or "greatest integer"
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
is it kinda like a piecewise function or something like tht
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh yeah i remember!
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
so if \(x>2\) but close to 2, then \([x]=2\)
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
so you have \[\lim_{x\to 2}2x2=42=2\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
to be more precise \[\lim_{x\to 2^+}2x2=42=2\]
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok! at first it seemed confusing but oh ok now i get it!
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
whereas \[\lim_{x\to 2^}2x2=41=3\] because if \(x<2\) but close to 2, then \([x]=1\)
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok! tht seems soo much easier now!
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
yes if you know what it means it is not hard here is a nice picture of \(y=2x[x]\) http://www.wolframalpha.com/input/?i=2xfloor%28x%29
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok! i get it! i have another question again hang on
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
so it says find the xvalues(if any) at which f is not continuous. which of the discontinuities are removable. f(x)= 1/ x^2+1
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
\[f(x)=\frac{1}{x^2+1}\] has no discontinuities, since it is a rational function and the denominator is never 0 since \(x^2\geq 0\) for any \(x\) you can see that \(x^2+1\geq 1\) no matter what \(x\) is, so this function has no discontinuities. as the denominator is never zero
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
oh ok thank you @satellite73
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
you are welcome enough math, study something else or do something more constructive
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
pretty much tht was my last problem! time to find a prayer for theology class! thank you @satellite73 and study for english test tomorrow on grapes of wrath
 one year ago

satellite73Best ResponseYou've already chosen the best response.1
good luck with the joads
 one year ago

abannavongBest ResponseYou've already chosen the best response.0
lolz thanks i have to find the intercalary chapters to write about :3 i dont even know what those r
 one year ago
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