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- Find T4(x) Taylor polynomial of degree 5 of the function f(x)=cos(x^3) at a=0Find the third-degree Taylor polynomial of f (x) = sin x atx = 0.Determine whether the following statement is true or false, and explain why. The Taylor polynomial of degree 4 for ƒ at 0 has the same fifth derivative as ƒ at 0.
- Find the 5th degree Taylor Polynomial centered at x=0. sin(2x) ln(1+x)Find the polynomial P1(x) = a0 + a1x whose value and slope agree with the value and slope of f(x) = cos x at the point x = 0. (a) Find the polynomial P2(x) = a0 + a1x + a2 x2 whose value and first two derivatives agree with the value and first two derivatives of f(x) = cos x at the point x = 0. This polynomial is called the second-degree Taylor polynomial of f(x) = cos x at x = 0. (b) Complete the table comparing the values of f(x) = cos x and P2(x). What do you observe? d) Find the third-degree Taylor polynomial of f(x) = sin x at x = 0.If y'=x3+y2, where y=1 when x=0, find a degree 3 polynomial that best fits the solution using Taylor Series Polynomial.