Answer:
[tex]\displaystyle \lim_{x \to -8} f(x) = 1[/tex]
General Formulas and Concepts:
Calculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Step-by-step explanation:
*Note:
When you graph the function, the left-hand and right-hand limit does equal the same.
Step 1: Define
[tex]\displaystyle f(x) = \left \{ {{x + 9, x < -8} \atop {-7 - x, x \geq -8}} \right.[/tex]
Step 2: Find Limit
- Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to -8} f(x) = \lim_{x \to -8} (-7 - x)[/tex]
- Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to -8} f(x) = -7 - (-8)[/tex]
- Simplify: [tex]\displaystyle \lim_{x \to -8} f(x) = 1[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
