Question

L'hopital's rule for limits approaching infinity

Answer 1

L'Hopital's Rule is a mathematical theorem that helps evaluate the limit of a function as it approaches infinity. It is used when taking the limit of an indeterminate form, such as 0/0 or ∞/∞.

Step-by-step explanation:

L'Hopital's Rule is a mathematical theorem that helps evaluate the limit of a function as it approaches infinity. It is used when taking the limit of an indeterminate form, such as 0/0 or ∞/∞. The rule states that if the limit of the ratio of the derivatives of two functions exists, then the limit of the original function can be found by taking the ratio of their derivatives.

Here is the step-by-step process for applying L'Hopital's Rule for limits approaching infinity:

1. Identify the limit of the function as it approaches infinity.
2. If the limit is in an indeterminate form, differentiate both the numerator and denominator of the function.
3. Take the limit of the ratio of the derivatives.
4. If the resulting limit exists, it is the value of the original limit.