4) Find the third degree Taylor polynomial centered at 1 for the function \(f(x) = \sqrt{2x^2 + 14}\), and use it to approximate \(\sqrt{22}\). \\ Notes: i) If your approximation isnt very accurate then you have clearly made a mistake. ii) \(22 = 2 \times 2^2 + 14\)
Added by Tanya F.
Close
Step 1
J(s) = √(2s + 4) J'(s) = (1/2)(2s + 4)^(-1/2) * 2 = (1/√(2s + 4)) J''(s) = (-1/4)(2s + 4)^(-3/2) * 2 = (-1/2)(2s + 4)^(-3/2) J'''(s) = (3/8)(2s + 4)^(-5/2) * 2 = (3/4)(2s + 4)^(-5/2) Show more…
Show all steps
Your feedback will help us improve your experience
Moses Obasola and 61 other Algebra 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
Use the second Taylor polynomial of $f(x)=\sqrt{x}$ at $x=4$ to approximate $\sqrt{4.06},$ and find a bound for the error in the approximation.
Taylor Polynomials and Infinite Series
Taylor Polynomials
Find the Taylor polynomial of degree $n$ centered at the number $a$. $f(x)=\sqrt{x}, \quad n=2, \quad a=4$
Derivatives
Linear Approximations and Taylor Polynomials
Use a sixth-degree Taylor polynomial centered at for the function $f$ to obtain the required approximation. Function $\quad$ Approximation $f(x)=\sqrt{x}, \quad c=4 \quad f(5)$
Series and Taylor Polynomials
Recommended Textbooks
Elementary and Intermediate Algebra
Algebra and Trigonometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD