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

`\displaystyle \lim_(x \to 4) (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`

Explanation:

Step 1: Define

Identify.

`\displaystyle \lim_(x \to 4) (x^2 - 2x - 8)/(x - 4)`

Step 2: Solve

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

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

Unit: Limits