Question

lim as x--> 0 of (xcscx) is...

Answer 1

rewrite as lim as x->0 x/sinx

then use L'Hospital. Derivative of the top over derivative of the bottom. Then you get:

lim x->0 1/cosx = 1

Answer 2

\[\lim_{x \rightarrow 0}x \csc(x)=\lim_{x \rightarrow 0}\frac{x}{\sin(x)}=\lim_{x \rightarrow 0}\frac{1}{\cos(x)}=1\]

Answer 3

What is L'Hospital's Theorem?

Answer 4

http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule

Answer 5

If \(\frac{f(x)}{g(x)}\) tends to a limit then \(\frac{f'(x)}{g'(x)}\) tends to the same limit.

Answer 6

the limit must first be an indeterminate before you can apply L'Hopsital's rule which means that you will get that the limit becomes 0/0 or infinity/infinity then you can apply L'Hospital's

Answer 7

If \(f(x)=g(x)=0 or\pm\infty\).

Answer 8

i just done understand the intermediate step

Answer 9

Sorry the limit of both are equal.

Answer 10

dont*

Answer 11

Basically, if you try to evaluate a limit and get 0/0 or \(\pm\infty/\pm\infty\), then use l'Hopital's rule.

Answer 12

OH! thank you so much, I understand now

Answer 13

No problem.

Answer 14

l'hospital is just taking the derivative of the numerator and the denominator seperately

Answer 15

Remember that this rule can also be applied to other indeterminate forms such as 1^infinity, 0^0, 0*+-infinity, infinity^0, and finally infinity - infinity. (L'Hoptial's Rule can be applied when the original limit of f(x)/g(x) results in one of these forms)

Answer 16

what about something like lim as x approaches 0 of (1-cos^2(2x))/(x^2)

Answer 17

We have another simple indeterminate form of 0/0 here. Just take the derivative of the numerator and the denominator separately and see if you come up with a real answer.

Answer 18

if the derivative of the denominator is 2x, wont that still be 0?

Answer 19

Yes. You may use L'Hospital's rule as many times as needed as long as your limit is still an indeterminate form each time. You will have a constant in the denominator after using it the second time.

Answer 20

oh ok
then just plug in zero?

Answer 21

Yes. You should end up with 4. :)

Answer 22

I got it!!!! THANK YOU