Infinite limits

[Violagirl]

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!

 

[Deleted member 4993]

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!

 

[Violagirl]

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.

 

[BigGlenntheHeavy]

$\displaystyle x^{2}-x \ = \ x(x-1).$

 

[Violagirl]

Oh I see now, thanks Glenn! Now if anyone could answer my question the second problem too, that would be fantastic!

 

[BigGlenntheHeavy]

$\displaystyle \lim_{x\to(1/2)^{+}} \ \frac{x}{cos(\pi x)} \ = \ -\infty \ and \ \lim_{x\to(1/2)^{-}} \ \frac{x}{cos(\pi x)} \ = \ \infty,$

$\displaystyle hence \ the \ limit \ doesn't \ exist.$