How to apply L'Hopital's Rule to evaluate the limit

The video tutorial explains how to solve a mathematical problem involving an indeterminate form using direct substitution and derivatives. Initially, direct substitution results in a 0/0 form, prompting the use of derivatives for both the numerator and denominator. The tutorial walks through the process of applying derivatives and concludes with a final calculation, resulting in a simplified answer.

What is the result of applying direct substitution to the given expression initially?

• 1/2

• 0/0

• 1/0

• 2/1

Why is it necessary to take the derivative of the numerator and denominator in this problem?

• To apply the chain rule

• To simplify the expression algebraically

• To find the limit at infinity

• To resolve the indeterminate form

What is the derivative of the numerator in this problem?

• 2 cosine of 2x

• x squared

• sine of x

• e to the x

What is the derivative of the denominator in this problem?

• x squared

• sine of x

• 2 cosine of 2x

• e to the x

What is the final result after applying direct substitution post-differentiation?

• 1/2

• 1/0

• 0/0

• 2/1