Question
The function $f(x)$ is approximated near $x=0$ by the third-degree Taylor polynomial\[P_{3}(x)=2-x-x^{2} / 3+2 x^{3}\]Give the value of(a) $f(0)$(b) $f^{\prime}(0)$(c) $f^{\prime \prime}(0)$(d) $f^{\prime \prime \prime}(0)$
Step 1
The coefficients of the terms in the Taylor series are given by the derivatives of $f(x)$ evaluated at $x=0$, divided by the factorial of the order of the derivative. Show more…
Show all steps
Your feedback will help us improve your experience
Justin Fernandez and 87 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The function f(x) is approximated near x=0 by the third degree Taylor polynomial. P3(x) = 2 - x - x^2/5 + 8x^3 Give the value of the following. Enter the exact answers. (a) f(0) = (b) f'(0) = (c) f''(0) = (d) f'''(0) =
Match the Taylor polynomial approximation of the function $f(x)=e^{-x^{2} / 2}$ with its graph. [The graphs are labeled (a)-(d).] Use a graphing utility to verify your results. $y=e^{-1 / 2}\left[\frac{1}{3}(x-1)^{3}-(x-1)+1\right]$
Series and Taylor Polynomials
Taylor Polynomials
Use a sixth-degree Taylor polynomial centered at for the function $f$ to obtain the required approximation. Function $\quad$ Approximation $f(x)=\ln x, \quad c=2 \quad f\left(\frac{3}{2}\right)$
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD