Answer:
[tex]\displaystyle 5[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Algebra I
- Terms/Coefficients
- Factoring
- Functions
- Function Notation
Calculus
Limits
Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Derivatives
Derivative Notation
Instantons Rate of Change
Step-by-step explanation:
Step 1: Define
Identify
f(x) = 2x² + x - 1
x = 1
Step 2: Find Change
- Substitute in variables [Instantaneous Rate of Change]: [tex]\displaystyle \lim_{x \to 1} \frac{f(x) - f(1)}{x - 1}[/tex]
- Substitute in function: [tex]\displaystyle \lim_{x \to 1} \frac{2x^2 + x - 1 - [2(1)^2 + 1 - 1]}{x - 1}[/tex]
- Simplify: [tex]\displaystyle \lim_{x \to 1} \frac{2x^2 + x - 1 - 2}{x - 1}[/tex]
- Combine like terms: [tex]\displaystyle \lim_{x \to 1} \frac{2x^2 + x - 3}{x - 1}[/tex]
- Factor: [tex]\displaystyle \lim_{x \to 1} \frac{(x - 1)(2x + 3)}{x - 1}[/tex]
- Simplify: [tex]\displaystyle \lim_{x \to 1} (2x + 3)[/tex]
- Evaluate limit [Limit Rule - Variable Direct Substitution]: [tex]\displaystyle 2(1) + 3[/tex]
- Simplify: [tex]\displaystyle 5[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
