100%(1)1 out of 1 people found this document helpful
This preview shows page 7 - 12 out of 13 pages.
(b) (5 points) Using this, or otherwise, determine if the infinite series∞%n=11nenis convergent or divergent.Solution:PLEASE TURN OVER0CuteEFmalluIruesT1HenceTeruconvergentLTenconvergentTnInIComparisonTest
Math 1BFinal (Practice 1), Page 7 of 125. Letf(x) =(x2+ 1)ex2.(a) (20 points) Calculate the Maclaurin series off(x).Be sure to include a generalterm.
(b) (5 points) Using this, or otherwise, determine the value off(2n)(0).
Math 1BFinal (Practice 1), Page 8 of 126. (25 points) Consider the differential equationy′= 9−y2. Graph the solutions with thefollowing initial conditions:y(0) =−2,y(0) = 1 andy(0) =−4. Be sure to label eachsolution carefully.Solution:PLEASE TURN OVERiyco4
Math 1BFinal (Practice 1), Page 9 of 127. (25 points) Find an equation for the orthogonal trajectory to the family of curvesy=1k−x+ 1(kany constant)which contains the point (1,2).Solution:PLEASE TURN OVER