Answer:
2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
Algebra I
- Terms/Coefficients
- Functions
- Function Notation
Calculus
Limits
Limit Rule [Constant]: [tex]\displaystyle \lim_{x \to c} b = b[/tex]
Definition of a Derivative: [tex]\displaystyle f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h}[/tex]
Step-by-step explanation:
Step 1: Define
Identify
f(x) = 2x - 5
Step 2: Differentiate
- [Limit] Substitute in x [Function f(x)]: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - f(x)}{\triangle x}[/tex]
- [Limit] Substitute in function: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2(x + \triangle x) + 5] - (2x + 5)}{\triangle x}[/tex]
- [Distributive Property] Distribute 2: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{[2x + 2\triangle x + 5] - (2x + 5)}{\triangle x}[/tex]
- [Distributive Property] Distribute negative: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{2x + 2\triangle x + 5 - 2x - 5}{\triangle x}[/tex]
- [Subtraction] Combine like terms: [tex]\displaystyle \lim_{\triangle x \to 0} \frac{2\triangle x}{\triangle x}[/tex]
- [Division] Simplify: [tex]\displaystyle \lim_{\triangle x \to 0} 2[/tex]
- Evaluate limit [Limit Rule - Constant]: [tex]\displaystyle 2[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
