Question

Evaluate the following limit: Limit as x goes to 0 of (sin(11x) - 11xcos(11x))/(11x - sin(11x)).

Answer 1

When we have a limit which goes to zero divided by zero or infinity divided by infinity, it is said to be in indeterminate form. For limits which have indeterminate form, we can apply L'Hopital's rule, which lets us take the derivative of the numerator and denominator of

Answer 2

The limit you are interested in can be written: limx→∞sin(1x)1x . Now, as x→∞ , we know that 1x→0 and we can think of the limit as.