Pick two of the given functions and determine up to the 5th degree Taylor polynomial: a. g(x) = 2xe* about x = -1 b. h(x) = cos (2x + n) about x = 0

.Given that 3 is a zero of the function f(x) = x' - 3x? + 4x – 12, find the 1.maining zeros then write the function as a product of linear factors (in factored form). (

Find the nth Maclaurin polynomial for the function. f(x) = tan x, n = 3 P3(x) =

Find the fourth degree Taylor polynomial for f(x)=cos c centered at c= pi/4. Use it to approximate cos 50 degrees to five decimal places. Write the actual error with at least one sifnificant digit.  Also use Taylor's Theorem to find the maximum possible error from this approximation.

a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. 1 f(x) = 1 --, a = 1; approximate 1.08

Write sin(1.5) by using the Taylor Polynomial of degree 4 of sinx, round your answer to 9 digits after the decimal sign and use 3. 141 592 653 589 793 2385

Let y=f(x) be a cubic polynomial with leading coefficient, a=1; containing the ordered pair (2,0) and a zero at x=2i. Find the function, f(x), that has these characteristics.

Determine the degree of each of the following polynomial functions. a. f(x) = 1 + x + x? + x³ Degree of f: b. g(x) = x' 2x? – 6 Degree of g: c. h(x) = x° + 2x' + 1 Degree of h: d. j(x) = x² – 4 Degree of j: