Answer:
[tex]\displaystyle 51[/tex]
General Formulas and Concepts:
Algebra I
- Terms/Coefficients
- Factoring
- Functions
- Function Notation
Algebra II
Calculus
Limits
- Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/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]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]
Step 2: Solve
- Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3[/tex]
- Factor: [tex]\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1][/tex]
- Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1[/tex]
- Evaluate [Limit Property - Variable Direct Substitution]: [tex]\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1][/tex]
- Simplify: [tex]\displaystyle 51[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
