Question

Please help!! i have no clue what to do and this packet is due tonight.

Answer 1

[C] 27

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

• Expand by FOIL
• Factoring

Calculus

Limits

Derivatives

Definition of a Derivative:
`\displaystyle f'(x) = \lim_(h \to 0) (f(x + h) - f(x))/(h)`

Explanation:

Step 1: Define

Identify

`\displaystyle \lim_(h \to 0) (f(3 + h) - f(3))/(h)`

`\displaystyle f(x) = x^3`

Step 2: Solve

1. Substitute in function value:
   `\displaystyle \lim_(h \to 0) ((3 + h)^3 - 3^3)/(h)`
2. Evaluate exponents:
   `\displaystyle \lim_(h \to 0) ((3 + h)^3 - 27)/(h)`
3. Expand:
   `\displaystyle \lim_(h \to 0) (h^3 + 9h^2 + 27h + 27 - 27)/(h)`
4. [Subtraction] Combine like terms:
   `\displaystyle \lim_(h \to 0) (h^3 + 9h^2 + 27h)/(h)`
5. Factor:
   `\displaystyle \lim_(h \to 0) (h(h^2 + 9h + 27))/(h)`
6. Simplify:
   `\displaystyle \lim_(h \to 0) h^2 + 9h + 27`
7. Evaluate limit:
   `\displaystyle 0^2 + 9(0) + 27`
8. Evaluate exponents:
   `\displaystyle 9(0) + 27`
9. Multiply:
   `\displaystyle 27`

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

Unit: Derivatives

Book: College Calculus 10e