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anonymous
 3 years ago
I need AP Calculus help!!
anonymous
 3 years ago
I need AP Calculus help!!

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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i will post the assignment soon!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the circled questions btw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0for the first one, its just 8 thats posted?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0its numbers 10, 14, 16, 18, 22

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh i was looking at the first one

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh man, that second one's really hard to read lol so lets do the first one

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0k so for 8 what is x approaching? i cant see

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0we dont have to do number 8 lol

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0:\ it looked circled to me lol

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0its only numbers 10, 14, 16, 18, 22

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0do you not have to do the problem in your first attachment?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah duh i forgot i do lolz

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0haha 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?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0number 8 its as x goes to infinity

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so it's as x> infinity of (2x^2)/(x^2 +3) ? is that right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0have y'all talked about L'Hospital's Rule yet?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0what is the L'hospitals rule? can u plz explain

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i don't think you're supposed to use it if you haven't covered it yet. you don't need it anyway.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so you start by considering the terms with the highest exponents

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0if 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so what would you have if you did that?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0hang on im kinda confused

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that's ok. so what i'm saying is your next step is to rewrite the limit excluding the +3 in the denominator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0to exclude the +3 in the denominator how do u do tht?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0because 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)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0in other words, the fraction approaches 1/2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0im sorry, it approaches 2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0because 2x^5 is in the numerator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok so ur limit is basically 2 then right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok now i get number 8

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0for 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0im kinda confused on tht part

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it's kind of counterintuitive at first

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0as 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0can u help me with the continuity limits and onesided ones those ones are the ones that r confusing

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i can help w one more then i need to get my own work done haha

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so i guess pick one for us to do

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i think i get the rest on my THQ but i need help with the continuity ones

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0let me post the problem

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{x \rightarrow 4} \frac{ \sqrt{x}2 }{ x4 } \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so first notice that when x = 4, f(x) = 0/0, which is undefined.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and 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?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0can u explain it a bit more im still a bit confused

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sure. 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)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah so its like it keeps on approaching 4 right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ya it keeps approaching 4

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but from the lessthan4 side because it has the minus sign (x>4)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0basically the limit for it will negative right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well the numerator and denominator are both negative, right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so the fraction comes out positive

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0why r limits soo confusing :3

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0lol i know. wanna see my limit problem that no one will answer?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Limit as x>(pi/2) of [tanx+1/(xpi/2)]?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thats my question that no one will answer :(

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i had it on a quiz today

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0can u do the substitution method for tht one

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0no because tan of pi/2 is undefined, it goes to neg infinity and infinity from the right and left....

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah ur right oops lol

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0but im still kinda confused on the continuity limits and onesided ones

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh boy satellite's here.... it's about to get real xD

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{ x\to\frac{\pi}{2}}\frac{\tan(x)+1}{x\frac{\pi}{2}}\]?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oooh well that's my problem but not hers

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0somewhere down the list!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@jldstuff393 how do u do my problem kinda confuzzled

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i know i know. u remember difference of squares? like (x^2  4) = (x2)(x+2)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is this the problem \[\lim_{x \rightarrow 4} \frac{ \sqrt{x}2 }{ x4 }\]?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh yeah i remember different of squares

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah @satellite73 thts my problem

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so 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)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0does that make sense?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the gimmick here is to "rationalize the numerator" by multiplying by the conjugate of \(\sqrt{x}2\) which is \(\sqrt{x}+2\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0cuz when u have that, you can cancel out the (sqrt(x)2) in the numerator and denominator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so u multpily the top and bottom by \[\sqrt{x} +2 \]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0this works because \((a+b)(ab)=a^2b^2\) and so \((\sqrt{x}2)(\sqrt{x}+2)=x4\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that cancels with the \(x4\) in the denominator, which is what you want, you want to cancel the zero

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and x4 can cancel in denominator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so ur limit is one right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0leaves you with \[\lim_{x \rightarrow 4} \frac{ \sqrt{x}2 }{ x4 }=\lim_{x \rightarrow 4} \frac{1 }{ \sqrt{x}+2}\]\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0no limit is not one, now you have to replace \(x\) by 4

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0once u replace x with 4 u get 1/ 4 right?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0whenever you get \(\frac{0}{0}\) you need some gimmick to factor and cancel to get rid of the zeros

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0satellite would you mind helping me after you're done here? O.o good luck guys!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sometime sit is easy sometimes it is a pain. but you get used to it

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@satellite73 i have some more questions!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@jldstuff393 sure if i can what is the question

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@abannavong go ahead and post them, i will look

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i'll repost it, thanks!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0kk! thanks @satellite73

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0number 14 its as deltax goes to 0 with the little plus sign

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i can't read 18 either is it \(\lim_{ x\to 1^+}\) or \(\lim_{x\to 1^}\)?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then replace \(x\) by 1 in the second formula you get \(11=0\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0can u help with 14 also

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sure, 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it is actually very straight forward we will do a little algebra and that is all

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0kk hang on dinner quickly

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok! @satellite73 im back from dinner

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0im eating and doing work lolz

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you are either eating late or are on the left coast

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0im on the west coast lolz

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0after 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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes exactly it is \((x+h)(x+h)=x^2+2xh+h^2\)

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that is all in the numerator you get \[\frac{2xh+h+h^2}{h}\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0and then can u factor out the h on the numerator

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes factor and cancel or divide each term by \(h\) it is the same thing

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok and then u get 2x+1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0whew that was exhausting

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is that an absolute value sign?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0or is that the floor function?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0its like a bracket and then two straight lines inside

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0do you know what that function is called?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ughhh i dont remember what it was called

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0it is either called "floor" or "greatest integer"

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0is it kinda like a piecewise function or something like tht

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so if \(x>2\) but close to 2, then \([x]=2\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so you have \[\lim_{x\to 2}2x2=42=2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0to be more precise \[\lim_{x\to 2^+}2x2=42=2\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok! at first it seemed confusing but oh ok now i get it!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0whereas \[\lim_{x\to 2^}2x2=41=3\] because if \(x<2\) but close to 2, then \([x]=1\)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok! tht seems soo much easier now!

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok! i get it! i have another question again hang on

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=\frac{1}{x^2+1}\] 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0oh ok thank you @satellite73

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0you are welcome enough math, study something else or do something more constructive

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0pretty 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0good luck with the joads

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