Calculus - Taylor

could you please help me with solving this problem?

#1) Find the Taylor polynomial Tn(x) for the function 'f' at the number 'a'.

f(x) = sqrt(3+x^2) ; a=1; n=2;

my work so far:

f (x) = sqrt(3+x^2) = (3+x^2)^(1/2)
f ' (x) = (1/2)(3+x^2)^(-1/2)
f '' (x) = (-1/4)(3+x^2)^(-3/2)
f ''' (x) = (3/8)(3+x^2)^(-5/2)

f (x) = 2
f ' (x) = 1/4
f '' (x) = -1/32
f ''' (x) = 3/256

T2(x) = (f(1)/0!)(x-1)^0 +(f(1)/1!)(x-1)^1 + (f(1)/2!)(x-1)^2
T2(x) = 2 + 1/4(x-1) + -1/64(x-1)^2
..do i solve for x???

which i tried..

0 = 2 + 1/4(x-1) + -1/64(x-1)^2
2 = 1/4x - 1/4 - 1/64x^2 + 1/32x - 1/64
8 = x - 1 - 1/16x^2 + 1/8x - 1/16
64 = 8x - 8 - 1/2x^2 + 1/8x - 1/16
72.5 = 9x - 1/2x^2
145 = 18x - 1x^2
-145 = -18x + x^2
145/18 = x + x^2
.. and im not sure where to go with this..

"T2(x) = 2 + 1/4(x-1) + -1/64(x-1)^2
..do i solve for x???"

The answer is T2(x) you just calculated.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Q.1)If one zero of the polynomial 3x2-kx-2 is 2 find the other zero.allso find the value of k. Q.2)If sum of the zeroes of the polynomial x2-x-k(2x-1) is 0,find the value of k Q.3)If 2 and 3 are the zeroes of the polynomial

  2. Calculus

    Find the 4th Taylor polynomial, P4, generated by f(x) = 1/x at center a = 2 ?

  3. Math

    The equation xy-1=x+y^2 defines a function y=f(x) in a neighborhood of (-1,0). Determine f(-1), fx(-1), and fxx(-1) and the second -taylor polynomial t2 (x) based around x=-1

  4. Calculus

    Find the degree 3 Taylor polynomial T3(x) of the function f(x)=(−3x+33)^4/3 at a=2.

  1. Calculus NEED HELP!

    Consider the following function. f(x) = e^(2 x^2), a = 0, n = 3, 0

  2. math

    Find the taylor polynomial of degree 3 for f(x)=1/x+2 F(x)=-1/x+2)

  3. Mathematics

    Springdale Junior High has two students, Ashley and Taylor, that qualified for the regional track meet in the 800 meter dash. The final race has only four spots available. Both Ashley and Taylor earned a spot in the final. There

  4. Calculus

    Consider the function f(x) = 10^x a) write the power series for f(x) centered at a = 2 using summation notation b) Suppose you wanted to estimate the function "f" at values of x in the interval [1.9,2.1] using the 4th degree

  1. calculus

    One more question... If you have f(x) = xsinx and the question is asking for the fourth degree Taylor polynomial about x=0, can you use the sinx Taylor polynomial series equation? I'm confused because there's the x in front so I

  2. Math

    How would you do this problem, I am stuck. Find the Taylor series of f(x)=1/x centered at x=2.

  3. Calculus

    Consider the following function. f(x) = e^(2 x^2), a = 0, n = 3, 0

  4. English

    1. To come up with possible solutions to a problem is referred to as: A. decision making. B. concept mapping. C. critical thinking. D. problem solving. is it D 2. "Should I apply for a job or go for an internship?" is an example

You can view more similar questions or ask a new question.