MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 10.1 Solutions Fa 2014

• School: Ohio State University
• Department: Mathematics
• Course: MATH 1172
• Professor: All

Document Summary

October 9, 2015: find linear and quadratic approximations to f (x) = x centered at the point a = 9. Use these polynomials to approximate the value of the function at x = 8. 9. Solution: f (x) = 1 linear approximation to f (x) = x centered at 9 is. So the slope of the tangent line at the point 9 is f (9) = 1. L(x) = f (9) + f (9)(x 9) = 3 + The linear approximation, l(x), gives us the following estimation of 8. 9. Thus the quadratic approximation to f (x) = x centered at 9 is. Q(x) = f (9) + f (9)(x 9) + The linear approximation, q(x), gives us the following estimation of 8. 9 (x 9)2 = 3 + (x 9) + (x 9)2 = 8 2. 98338: find the nth order taylor polynomial centered at 0 for n = 0, 1, 2 of the function f (x) = tan(x).