10.2 Taylor SeriesDan Jones2025-02-24T14:28:09-06:00

10.2 Taylor Series

1. If f(1) = 3, f '(1) = -6, f ''(1) = 4 and f '''(1) = -7 find the P3 Taylor Polynomial or the Cubic approximation for f(x) centered at x = 1. b) Then use it to approximate f(1) and f(1.3)

2. Find the T5 Taylor Polynomial for f(x) = sin x centered at x = π/6

Graphically

3. Use the T5(x) approximation for sin x at x = π/6 to approximate sin(.7)

4. Find the Maclaurin Polynomials (c = 0) for cos x (first 4 non-zero terms). Then use it to approximate cos(0.1).

Find th fifth degree Maclaurin Polynomial for e^x and use it to approximate e^0.2

Find Maclaurin for e^(x^3) and integrate the series between 0 and 1

Find P19 Maclaurin series for 3x•sin(x^2)

Find Maclaurin for cos(x^(3/2)) and use it to solve a differential equation.

Find a Taylor Series given a derivative generator

Combining 2 Maclaurins by addition