Question

Find the indicated limit, if it exists.

Answer 1

`\displaystyle \lim_(x \to -8) f(x) = 1`

General Formulas and Concepts:

Calculus

Limits

Limit Rule [Constant]:
`\displaystyle \lim_(x \to c) b = b`

Limit Rule [Variable Direct Substitution]:
`\displaystyle \lim_(x \to c) x = c`

Limit Property [Addition/Subtraction]:
`\displaystyle \lim_(x \to c) [f(x) \pm g(x)] = \lim_(x \to c) f(x) \pm \lim_(x \to c) g(x)`

Explanation:

*Note:

When you graph the function, the left-hand and right-hand limit does equal the same.

Step 1: Define

`\displaystyle f(x) = \left \{ {{x + 9, x < -8} \atop {-7 - x, x \geq -8}} \right.`

Step 2: Find Limit

1. Substitute in function [Limit]:
   `\displaystyle \lim_(x \to -8) f(x) = \lim_(x \to -8) (-7 - x)`
2. Evaluate limit [Limit Rule - Variable Direct Substitution]:
   `\displaystyle \lim_(x \to -8) f(x) = -7 - (-8)`
3. Simplify:
   `\displaystyle \lim_(x \to -8) f(x) = 1`

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

Unit: Limits