Enter the coefficients of the fifth taylor polynomial t5(x) for the function f(x) = x5−3x4+2x2+5x−2 based at b=1. t5(x)= + (x−1)+ (x−1)2+ (x−1)3+ (x−1)4+ (x−1)5. note: this exercise gives a method for writing a polynomial in powers of x−1 instead of powers of x. this may be useful, for example, if you are interested in the values of the polynomial near x=1 .

The coefficients are 3, 2, -6, -2, 2, and 1 and this can be determined by using the series formula.

Given :

The formula of the series is given below:

Now, determine the value of .

Now, determine the value of .

Now, determine the value of .

Now, determine the value of .

The coefficients are 3, 2, -6, -2, 2, and 1 and this can be determined by using the series formula.

For more information, refer to the link given below:

link

Compute the necessary values/derivatives of at :

Taylor's theorem then says we can "approximate" (in quotes because the Taylor polynomial for a polynomial is another, exact polynomial) at by

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Another way of doing this would be to solve for the coefficients in

by expanding the right hand side and matching up terms with the same power of .

answer: $34.31

step-by-step explanation:

$11.99 x 3 = $35.97

$35.97 - 10% = $32.37

$32.37 + 6% = $34.31