Question
Suppose $f(2)=1, f^{\prime}(2)=1, f^{\prime \prime}(2)=0,$ and $f^{(3)}(2)=12.$ Find the third-order Taylor polynomial for $f$ centered at 2 and use this polynomial to estimate $f(1.9)$.
Step 1
Step 1: The third-order Taylor polynomial for a function $f$ centered at $a$ is given by the formula: \[p_{3}(x)=f(a)+f'(a)(x-a)+\frac{f''(a)}{2!}(x-a)^{2}+\frac{f^{(3)}(a)}{3!}(x-a)^{3}\] Show more…
Show all steps
Your feedback will help us improve your experience
Jack Chen and 100 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
Suppose $f(0)=1, f^{\prime}(0)=0, f^{\prime \prime}(0)=2,$ and $f^{(3)}(0)=6 .$ Find the third-order Taylor polynomial for $f$ centered at 0 and use it to approximate $f(0.2)$.
Power Series
Approximating Functions with Polynomials
Use a sixth-degree Taylor polynomial centered at for the function $f$ to obtain the required approximation. Function $\quad$ Approximation $f(x)=\ln x, \quad c=2 \quad f\left(\frac{3}{2}\right)$
Series and Taylor Polynomials
Taylor Polynomials
Suppose $f(0)=1, f^{\prime}(0)=2,$ and $f^{\prime \prime}(0)=-1 .$ Find the quadratic approximating polynomial for $f$ centered at 0 and use it to approximate $f(0.1)$.
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD