Question

Please someone help its calculus and i need #2! Its finding instantaneous rate of change!

Answer 1

`\displaystyle 5`

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
• Functions
• Function Notation

Calculus

Limits

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

Derivatives

Derivative Notation

Instantons Rate of Change

Explanation:

Step 1: Define

Identify

f(x) = 2x² + x - 1

x = 1

Step 2: Find Change

1. Substitute in variables [Instantaneous Rate of Change]:
   `\displaystyle \lim_(x \to 1) (f(x) - f(1))/(x - 1)`
2. Substitute in function:
   `\displaystyle \lim_(x \to 1) (2x^2 + x - 1 - [2(1)^2 + 1 - 1])/(x - 1)`
3. Simplify:
   `\displaystyle \lim_(x \to 1) (2x^2 + x - 1 - 2)/(x - 1)`
4. Combine like terms:
   `\displaystyle \lim_(x \to 1) (2x^2 + x - 3)/(x - 1)`
5. Factor:
   `\displaystyle \lim_(x \to 1) ((x - 1)(2x + 3))/(x - 1)`
6. Simplify:
   `\displaystyle \lim_(x \to 1) (2x + 3)`
7. Evaluate limit [Limit Rule - Variable Direct Substitution]:
   `\displaystyle 2(1) + 3`
8. Simplify:
   `\displaystyle 5`

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

Unit: Derivatives

Book: College Calculus 10e