Infinite limits

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Violagirl

Junior Member
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Mar 9, 2008
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I am not sure how to find the limit for this problem:

1.lim X^2-X/(X^2+1)(X-1) The problem was worked out in my book but what I am not sure of is how you would cancel out (X-1) to get to X/X^2+1.
x-->1

On this second one, I understand why a limit would not exist but am not sure how you determine it without a calculator. I'm thinking it has to do with one of the properties from Trig but am not for sure.

2. lim x sec TT X.
x--->1/2

Any help is greatly appreciated! :)
 
Violagirl said:
I am not sure how to find the limit for this problem:

1.lim X^2-X/(X^2+1)(X-1) The problem was worked out in my book but what I am not sure of is how you would cancel out (X-1) to get to X/X^2+1.
x-->1

Please use parenthesis to group operations correctly. The way you posted it - the function is:
\(\displaystyle X^2 - \frac{X}{X^2+1}\cdot (X-1)\)

Is this the correct function?

On this second one, I understand why a limit would not exist but am not sure how you determine it without a calculator. I'm thinking it has to do with one of the properties from Trig but am not for sure.

2. lim x sec TT X.
x--->1/2

Hint:

\(\displaystyle sec(\theta) = \frac{1}{cos(\theta)}\)

and

\(\displaystyle cos(\frac{\pi}{2}) = 0\)

Any help is greatly appreciated! :)
Click to expand...
 
For the first one, X^2-X is in the numerator and (X^2+1) (X-1) are in the denominator when starting out the problem.
 
Oh I see now, thanks Glenn! Now if anyone could answer my question the second problem too, that would be fantastic! :D
 
\(\displaystyle \lim_{x\to(1/2)^{+}} \ \frac{x}{cos(\pi x)} \ = \ -\infty \ and \ \lim_{x\to(1/2)^{-}} \ \frac{x}{cos(\pi x)} \ = \ \infty,\)

\(\displaystyle hence \ the \ limit \ doesn't \ exist.\)
 
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