Taylor polynomial T3(x) for; f(x)= 1/x center=2 a) Graph functions f and T 3 ove

Question

Taylor polynomial T3(x) for;

f(x)= 1/x center=2

a) Graph functions f and T3 over the domain [1/4, 4]. Plot points at x=1/4, 1, 2.5, 4.

b) Find the expression for the error. How is Z defined?

c). Suppose we focus on the specific value x = 2.5.

     i.   Find f(2.5).

     ii. Find T3(2.5).

     iii. Use results in i and ii   to determine the actual error

d) What is the reason for using a series with center c =2 when seeking to approximate f(2.5)?

a) Graph functions f and T3 over the domain [1/4, 4]. Plot points at x=1/4, 1, 2.5, 4.

b) Find the expression for the error. How is Z defined?

c). Suppose we focus on the specific value x = 2.5.

     i.   Find f(2.5).

     ii. Find T3(2.5).

     iii. Use results in i and ii   to determine the actual error

d) What is the reason for using a series with center c =2 when seeking to approximate f(2.5)?

Explanation / Answer

a. T3(x)= 0.5x-0.25(x-2)+0.125(x-2)^2 - (1/16)(x-2)^3   .....simply taylor expansion till 3rd term...

you can plot this in matlab and 1/x also.

b. error is difference: Z= (1/x - t3x)

c. f(2.5)= 1/2.5 = .4 while T3(2.5)= .3984375

the error is f(2.5)- T3(2.5)=.0015625

d. we are jus approximating the 1/x around x=2 as polynomial form..taylor expansion will not give the exact result as f(2.5) but an approximate result around analytic point...for any query contact me

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