MATH 1172 Midterm: MATH 1172 Ohio State University Math 1172 12.6 Solutions Fa 2014

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

Document Summary

1 find the rst and second derivative of the following function: compute the inde nite integral of the function r(t) = (cid:28)3 t, 2t6, The second derivative is found by taking the derivative of each component of the derivative. 2. di erentiate the following function r(t) = he(t2), sin(7t), ln(tan(t))i. Solution: to nd the derivative of a vector valued function take the derivative of each com- ponent. = (cid:28)2te(t2), 7 cos(7t), tan(t) sec2(t)(cid:29) sin(t) cos(t)(cid:29) . Solution: to compute the integral of a vector valued function we need to integrate each com- ponent. Using integration by parts with u = t, du = dt, dv = et dt, and v = et, we have. Z tet dt = tet z etdt = (t 1)et + c1. Using a u-substitution with u = t4, du = 4t3dt, we have. 1 t2 + 1 dt = arctan t + c3. Z r(t) dt = (cid:28)(t 1)et, 1.