Mr. Vu can drive his new electric car 194 miles before he needs to charge his battery. How far can Mr. Vu’s car go on 15 battery
1 answer:
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Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
- Left to Right<u> </u>
<u>Algebra I</u>
- Functions
- Function Notation
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative Rule [Quotient Rule]:
Derivative Rule [Chain Rule]:
MacLaurin/Taylor Polynomials
- Approximating Transcendental and Elementary functions
- MacLaurin Polynomial:
- Taylor Polynomial:
Step-by-step explanation:
*Note: I will not be showing the work for derivatives as it is relatively straightforward. If you request for me to show that portion, please leave a comment so I can add it. I will also not show work for elementary calculations.
<u />
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = ln(1 - x)
Center: x = 0
<em>n</em> = 3
<u>Step 2: Differentiate</u>
- [Function] 1st Derivative:
- [Function] 2nd Derivative:
- [Function] 3rd Derivative:
<u>Step 3: Evaluate Functions</u>
- Substitute in center <em>x</em> [Function]:
- Simplify:
- Substitute in center <em>x</em> [1st Derivative]:
- Simplify:
- Substitute in center <em>x</em> [2nd Derivative]:
- Simplify:
- Substitute in center <em>x</em> [3rd Derivative]:
- Simplify:
<u>Step 4: Write Taylor Polynomial</u>
- Substitute in derivative function values [MacLaurin Polynomial]:
- Simplify:
Topic: AP Calculus BC (Calculus I/II)
Unit: Taylor Polynomials and Approximations
Book: College Calculus 10e