Question

When using a calculator to apply L'Hôpital's Rule to evaluate the limit of an indeterminate form, which steps are typically involved

A) Substitute the values directly.
B) Simplify the expression algebraically.
C) Take the derivative of the numerator and denominator separately.
D) Use numerical methods to approximate the limit.

Answer 1

To apply L'Hôpital's Rule using a calculator, one must substitute values, simplify algebraically, take the derivative of the numerator and denominator separately, and possibly use numerical methods to approximate the limit.

Step-by-step explanation:

When using a calculator to apply L'Hôpital's Rule to evaluate the limit of an indeterminate form, the typical steps involved are:

1. Substitute the values directly.
2. Simplify the expression algebraically.
3. Take the derivative of the numerator and denominator separately. This is a critical step, as L'Hôpital's Rule requires you to take the limit of the ratio of the derivatives when the original limit produces an indeterminate form like 0/0 or ∞/∞.
4. Use numerical methods to approximate the limit if necessary.

Steps such as eliminating terms to simplify the algebra and checking the answer to see if it is reasonable are fundamental when solving problems in calculus. The use of a calculator, such as a TI-83 or 84 series, can greatly aid in performing the necessary calculations more efficiently.