MATH 111 Final: MATH 111 Amherst S14M111Final

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 111
• Professor: All

Document Summary

Read this first: please read each question carefully. Final exam: find the derivatives of the following functions. (a) h(w) = w5 + 5w (b) k( ) =r +q + sin . Final exam (c) g(t) = t(et). (use logarithmic di erentiation!) [5] (d) f (x) = ln eln x 1 + ex. Pay attention to whether they are de nite or inde nite. (a) 0 xpx2 + a2 dx, a > 0. Evaluate the integralz the result as an area. Final exam tp36 t4 dt by rst performing a substitution and then interpreting. Use the - de nition of a limit to show lim x 1/2. Use the de nition of derivative to nd f (x) for f (x) = State the integral de nition of the function ln(x), and use it to compute the derivative of ln(x) by appealing to an appropriate theorem. Use part (a) and the de nition of a derivative to evaluate the limit.