1.

The Taylor series, centered at 0, of the function at) 2 8 cos (73:2) can be written as f (m): :0 an 3:\" where a few of the coefficients are: Find T4($): the Taylor polynomial of degree 4 of the function an) = arctan(8:c) at a = 0. (You need to enter a function.) W) = :J Find T5($): the Taylor polynomial of degree 5 of the function an) = sin(43:) at a = 0. (You need to enter a function.) w = :J Find T3($): the Taylor polynomial of degree 3 of the function an) = cosmic) at a = 0. (You need to enter a function.) w = :J Find the degree 3 Taylor polynomial T3 (x) of function f(a) = (3x + 69) at a = 4. T3 (20) =Find T5 (3:): Taylor polynomial of degree 5 of the function f(:n) = cos(:n) at a, = 0. W) = :1 Using the Taylor Remainder Theorem, find all values of x for which this approximation is within 0.002638 of the right answer. Ms C] Assume that sin(x) equals its Maclaurin series for all x. Use the Taylor series centered at 0 for sin (532) to evaluate the integral 0.66 f sin(5a:2) da: 0 Your answer will be an infinite series. Use the first two terms to estimate its value. :] The Taylor series for f(x) = e at a = 3 is Cn (2 - 3 ) n n=0 Find the first few coefficients. CO = C2 C3 C4Let P ( 2, 4, 3) and Q (1, 2, 2) be two points. Find the distance between P and Q. Enter your answer as an expression. :1 Write an equation for a sphere centered at the point (6,-2,-1) with radius 5. :1 The equations :32 + y2 + 22 22: = 0 and :32 14w + y2 + 10y + z2 = 58 represent spheres in three dimensions. Find the distance between these two spheres. Include at least three decimal places in your