Old Exam 3 with Answer Key - Calculus and Analytic Geometry | MATH 221, Exams of Analytical Geometry and Calculus

Download Old Exam 3 with Answer Key - Calculus and Analytic Geometry | MATH 221 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! 1 Exam 3 A. Miller Fall 91 Math 221 1.(8%) Find the area of the region bounded by the curves y = x2 and x+y = 6. 2.(9%) Find the x coordinate of the center of mass of a thin homogeneous plate covering the region bounded by the curves y = x2 and x + y = 6. 3.(8%) Find dydx if y = log2(x 4). 4.(9%) Find the volume generated by revolving the region bounded by y = √ x and the lines y = 1 and x = 0 about the line y = 1. 5.(8%) Find dydx if y = 2 ln(x). 6.(9%) Find the volume generated by revolving the set of all points (x, y) with 0 ≤ x ≤ 1 and 0 ≤ y ≤ x2 − x3 about the y-axis. 7.(8%) Find dydx if y = arctan(ln(x)). 8.(9%) Find the area of the surface generated by revolving the curve x = y2 +1 for 1 ≤ y ≤ 2, about the x-axis. 9.(8%) Find the average value of the function ln(x)/x on the interval [1, 5]. 10.(8%) Evaluate the integral ∫ 2 0 x2 1+x6 dx. 11.(8%) Evaluate the integral ∫ 1 0 ex 1+ex dx. 12.(8%) In Benjamin Franklin’s will he estimated that his bequest of 1000 pounds would grow to 131,000 pounds in 100 years. He was using an annual rate of 5% and compounding once each year. What rate of interest per year compounding continuously for 100 years would multiply the original amount to 131,000 pounds?