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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 C4The 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