MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 10.3 & 10.4 Fa 2014a

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

Document Summary

October 20, 2015: (test problem) true or false: suppose f (x) = x3 + 2x2. [hint: the taylor series for sin(x) centered at 0 may be useful. ] + 5: consider the function f (x) = sin(3x) and the remainder in the taylor series centered at the point 0 for f (x). Show that limn rn(x) = 0 for all x in r. Taylor series about 0 for the given function. Then identify the function represented by the di erentiated series and give the interval of convergence of the derivative: f (x) = sin(x2), use taylor series to approximate the following de nite integral with an error less than 10 4. e(x2)dx. 0: f (x) = tan 1 x, (test question) find the rst four nonzero terms of the taylor series centered at a = 0 for the f (x) = x2 ln(1 + x3).