(Will not be accepted without staple) [First Name] [Last Name] Math-2417, thq 08, 13-10-16, 10:13 [Net ID] [Problem Section] Instructions: 1. Fill in the requested information on the line above. 2. This handout is due at the beginning of problem section. 3. This handout must be printed out and stapled. You may print it double sided. 4. Your work must be hand written on this handout. 5. You must show all work. You may receive zero or reduced points for insufficient work. 6. Your work must be neatly organized and written. You may receive zero or reduced points for sloppy work. 7. Only a subset of these questions will be graded. You will not be told which questions will be graded in advance. Page 2 of 9 Questions 1 2 3 4 5 6 7 8 Total Points 10 10 10 10 10 10 10 10 30 Score 1. (10 points) Evaluate the integrals. (a) Z4 (3 Z (x2 1 (b) |x Math-2417, thq 08, 13-10-16, 10:13 3|) dx 9)3 (2x)dx Page 3 of 9 2. (10 points) Evaluate the integrals. Z 1 1 (a) cos d 2 (b) Z 2x + 1 p dx x+4 Math-2417, thq 08, 13-10-16, 10:13 Page 4 of 9 Math-2417, thq 08, 13-10-16, 10:13 3. (10 points) Find the area of the region bounded by the graphs of the equations. p (a) y = x2 3 x + 2, (b) y = sec2 x 2 , x= 2, x= , 2 x = 6, x= 2 , 3 y = 0. y = 0. Page 5 of 9 4. (10 points) Let F (x) = Z Math-2417, thq 08, 13-10-16, 10:13 x f (t)dt, where f is the function whose graph is shown in the figure. 0 (a) Find the largest open interval on which F is increasing. (b) Find the largest open interval on which F is decreasing. Page 6 of 9 5. (10 points) Find F 0 (x). (a) F (x) = Zx2 1 dt t3 2 x+2 Z (b) F (x) = (4t + 1)dt x Math-2417, thq 08, 13-10-16, 10:13 Page 7 of 9 Math-2417, thq 08, 13-10-16, 10:13 6. (10 points) Determine whether the statement is true or false. Explain your conclusion. Z (a) 4 sin x cos xdx = cos 2x + C (b) Z1 1 x 2 dx = x 1 1 1 = ( 1) 1= 2 Page 8 of 9 Math-2417, thq 08, 13-10-16, 10:13 7. (10 points) (a) Find the limit. x lim ln p x!5+ x 4 (b) Find the equation of the tangent line to the graph of f at the give point. f (x) = sin(2x) ln(x2 ), (1, 0) Page 9 of 9 8. (10 points) Use logarithmic dierentiation to find dy/dx. y= (x + 1)(x 2) , (x 1)(x + 2) x>2 Math-2417, thq 08, 13-10-16, 10:13