Question

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0+ cot(2x) sin(4x).

Answer 1

The limit of cot(2x) sin(4x) as x approaches 0+ is 0.

Step-by-step explanation:

To find the limit of cot(2x) sin(4x) as x approaches 0+, we can use l'Hospital's Rule. We can rewrite the expression as cos(2x)/sin(2x) * sin(4x). Taking the derivative of the numerator and denominator, we get -2sin(2x)/2cos(2x) * sin(4x). Simplifying, we have -sin(2x) * sin(4x). Now, plugging in x = 0, we get 0. Therefore, the limit is 0.