Question

find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→4 x2 − 2x − 8 x − 4

Answer 1

Answer:

$\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4} = 6$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

Terms/Coefficients

• Factoring

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             $\displaystyle \lim_{x \to c} x = c$

Step-by-step explanation:

Step 1: Define

Identify.

$\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4}$

Step 2: Solve

1. [Limit] Rewrite [Factoring]:                                                                             $\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4} = \lim_{x \to 4} \frac{(x - 4)(x + 2)}{x - 4}$
2. [Limit] Simplify:                                                                                               $\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4} = \lim_{x \to 4} x + 2$
3. Limit Rule [Variable Direct Substitution]:                                                     $\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4} = 4 + 2$
4. [Order of Operations] Evaluate:                                                                   $\displaystyle \lim_{x \to 4} \frac{x^2 - 2x - 8}{x - 4} = 6$

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

Unit: Limits