Find limit. Please answer

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Constant]:                                                                                            

Limit Rule [Variable Direct Substitution]:                                                            

Limit Property [Addition/Subtraction]:                                                                  

L'Hopital's Rule

Differentiation

Basic Power Rule:

Step-by-step explanation:

We are given the following limit:

Substituting in x = 2 using the limit rule, we have:

Evaluating the result, we get an indeterminate form:

Since we have an indeterminate form, let's apply L'Hopital's Rule. Differentiate both the numerator and denominator respectively:

Simplify:

Evaluate the limit using the limit rule:

Simplify:

And we have our answer.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits