anonymous
  • anonymous
what is this limit \[\lim_{x \rightarrow \pi/2}(xcosx)\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\lim_{x \rightarrow \pi/2}(xcosx)\]
Mertsj
  • Mertsj
0
anonymous
  • anonymous
mertsj do you mind demonstrating that please?

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Mertsj
  • Mertsj
pi/2times cospi/2=pi/2times 0 = 0
anonymous
  • anonymous
ok thanks would you mind helping me with this one also
anonymous
  • anonymous
\[\lim_{x \rightarrow -7}(x^2 + 10x + 21/x + 7)\] i've got -98/0. i dont know what to do from there
Mertsj
  • Mertsj
You can't divide by 0 so divide numerator so another approach is needed.
Mertsj
  • Mertsj
Factor and reduce first
anonymous
  • anonymous
ok i was thinking along the lines as approach -7 from left and right
anonymous
  • anonymous
(x+7)(x+3)/(x+7)...so the x + 7 cancels and im left with x + 3
Mertsj
  • Mertsj
yes
Mertsj
  • Mertsj
Now replace the x with -7
anonymous
  • anonymous
i see.
anonymous
  • anonymous
i have this one that is somewhat similar but you end up with 0/0 \[\lim_{x \rightarrow 1}(x^2 - 4x + 3/ x^2 + 2x -3)\]
anonymous
  • anonymous
same approach again right? factor and reduce?
Mertsj
  • Mertsj
yes
anonymous
  • anonymous
(x-3)(x-1)/ (x-3)(x+1)...?
anonymous
  • anonymous
is that the right structure
Mertsj
  • Mertsj
|dw:1326943979278:dw|
anonymous
  • anonymous
oh wow im getting this thanks for the help. would you be willing to continue working with me? i have about 8 more
Mertsj
  • Mertsj
I am willing but I might be a little distracted as my daughter is here and we are visiting.
anonymous
  • anonymous
ok no problem
anonymous
  • anonymous
\[\lim_{x \rightarrow -10}(x^2 - 17x + 70/ x + 10)\]
anonymous
  • anonymous
when i attempt this...
anonymous
  • anonymous
i get 140/0...so i take the factor and reduce approach
anonymous
  • anonymous
and..
Mertsj
  • Mertsj
Yes factor and reduce
Mertsj
  • Mertsj
|dw:1326944396601:dw|
anonymous
  • anonymous
(x+10)(x+7)/ (x+10)....x+7...-10+7= -3?
anonymous
  • anonymous
i keep getting my signs wrong when i factor
Mertsj
  • Mertsj
It won't reduce. Did you copy it right?
anonymous
  • anonymous
why couldnt it have been (x+10)(x+7)...it will also give you 70 right
Mertsj
  • Mertsj
Middle term is negative
anonymous
  • anonymous
yeah thats right i remember now
Mertsj
  • Mertsj
Did you copy it right?
anonymous
  • anonymous
what do you mean
anonymous
  • anonymous
it does not exist
anonymous
  • anonymous
i see that
Mertsj
  • Mertsj
Perhaps you wrote the problem down incorrectly
anonymous
  • anonymous
yeah now i understand
anonymous
  • anonymous
i have this next one...
Mertsj
  • Mertsj
Did you get that last one?
anonymous
  • anonymous
yeah
Mertsj
  • Mertsj
What did you get?
anonymous
  • anonymous
\[\lim_{x \rightarrow 2}(x^2 - 4/2x^2 -5x + 2)\]
anonymous
  • anonymous
I got DNE (does not exist) my software accepted the answer
anonymous
  • anonymous
how exactly would you factor the denominator in the previous problem. it is set up strangely for me
Mertsj
  • Mertsj
That one should factor and reduce.
Mertsj
  • Mertsj
(2x-1)(x-2)
anonymous
  • anonymous
ok i was confused because i thought somehow it must add up to -5
Mertsj
  • Mertsj
So you end up with (x+2)/(2x-1)
anonymous
  • anonymous
gotcha
anonymous
  • anonymous
next is...
anonymous
  • anonymous
\[\lim_{x \rightarrow 4}(\sqrt{b+0}-2/b-4)\]
anonymous
  • anonymous
0/0
anonymous
  • anonymous
do you still factor here? doesnt look like it
Mertsj
  • Mertsj
It won't factor but why does it have sqrt(b+0) since that is just sqrt(b)?
anonymous
  • anonymous
its sqrt (b +0)...i would guess you do 4 +0 then squared root your answer then subtract 2
Mertsj
  • Mertsj
But the denominator will be 0 and that is undefined.
anonymous
  • anonymous
yeah i got 0/0 i was thinking theres something we could do next
Mertsj
  • Mertsj
multiply the numerator and denominator by (sqrt(b)+2)
anonymous
  • anonymous
if the numerator and denominator are both zeros. wouldnt mulitplying bring us back to square 1 with 0/0
Mertsj
  • Mertsj
|dw:1326945956921:dw|
anonymous
  • anonymous
i see
anonymous
  • anonymous
|dw:1326946154087:dw|
anonymous
  • anonymous
the limit is as x approaches -9
Mertsj
  • Mertsj
Multiply numerator and denominator by 9x
Mertsj
  • Mertsj
|dw:1326946478456:dw|
Mertsj
  • Mertsj
lim as x approaches -9 is -1/81
anonymous
  • anonymous
thanks im almost through
anonymous
  • anonymous
Let 11x−36≤f(x)≤x2+5x−27 . Use the Squeeze Theorem to determine limx→3f(x) =
Mertsj
  • Mertsj
ok but I still want to revisit that DNE one
anonymous
  • anonymous
ok when we finish we can go back
anonymous
  • anonymous
this one that i posted is a new concept so its unlike what we have been practicing so im clueless
Mertsj
  • Mertsj
I see that. I have never heard of the squeeze theorem but I would assume that we should evaluate both expressions when x is 3
anonymous
  • anonymous
i got 33 and -3 respectively. what do i do with these two numbers to come up with a final answer
Mertsj
  • Mertsj
You should get -3 for both of them and that is the limit. I just read it on the internet.
Mertsj
  • Mertsj
redo the one you got the 33 for
anonymous
  • anonymous
yeah you're right i entered it incorrectly in my calculator
anonymous
  • anonymous
|dw:1326947257959:dw| as x approaches 0
Mertsj
  • Mertsj
I'm not sure about this one. Unless you use a reduction formula of some sort.
anonymous
  • anonymous
ok
Mertsj
  • Mertsj
Have you tried typing it into wolframalpha?
TuringTest
  • TuringTest
L'hospital does this one easily
anonymous
  • anonymous
|dw:1326947625929:dw|
Mertsj
  • Mertsj
Well let's see it.
anonymous
  • anonymous
as x approaches 0
Mertsj
  • Mertsj
I'll turn you over to Turing now.
anonymous
  • anonymous
thanks for all the help Mertsj I really appreciate it
Mertsj
  • Mertsj
yw
Mertsj
  • Mertsj
Ask turing about that other one also
anonymous
  • anonymous
ok I hope to see you around again. Enjoy
TuringTest
  • TuringTest
@mertsj, yes, well, done @Jinnie: do you know L'hospital's rule? derivative of top and bottom gives \[\frac{9\cos(9x)}{1}\]
Mertsj
  • Mertsj
Thanks
anonymous
  • anonymous
hey turningtest thats my first time hearing about that rule
TuringTest
  • TuringTest
can you take the derivative of sin(9x) ?
anonymous
  • anonymous
no i dont know how
TuringTest
  • TuringTest
Then you can't use L'hospital, which unfortunately means I can't help you as well as I hoped. I can tell you that \[\lim_{x \rightarrow 0}\frac{\sin x}{x}=1\]but proof of that are bit complicated without L'hospital's rule. All I can suggest is to try to use that fact to help you. anyway the answer is that the limit in your question is 9
anonymous
  • anonymous
ok, would you be willing to do several more of these and I ask my professor about this rule next class?
TuringTest
  • TuringTest
have you learned derivatives yet at all?
anonymous
  • anonymous
nah we just started school last week
anonymous
  • anonymous
|dw:1326948473758:dw| lim as x approaches 0. this is all i need help with
TuringTest
  • TuringTest
then all I can do is give answers without explanation, because the way I solve these is with a method you don't know. If you just want the answer I refer you to wolfram alpha as mertsj did. Here is your question posted there: http://www.wolframalpha.com/input/?i=limit+x+to+0+sin%289x%29%2Fx learn to use this site, but it will not help you understand, so don't rely on it.
TuringTest
  • TuringTest
this last one is 1/3 try typing it into wolfram to see if I'm right
anonymous
  • anonymous
alright thanks for the help
anonymous
  • anonymous
im done thanks to all
anonymous
  • anonymous
good night hope to see everyone again
TuringTest
  • TuringTest
goodnight :)

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