Name Instructions: Your exam must be submitted through Activities and Assessments/Assignments in LEO. You may use your textbook on this exam. . To receive full credit, you must show your work. . Please write neatly. Illegible answers will be assumed to be incorrect. This exam is worth 200 points. Good Luck! 1. Evaluate each limit. a) lim- X'-x-2 x+2 X-2 b) lim- t cos (t) 1+0 t2+t c) In x lim - X-00 X+1 2. Compute each derivative a) D(x4 - 5 tan(x) + In x) b) D(x3ex) x 2 () ax sin(x) 3. Determine y' at (0,2) for y2 +2y = 2sin(x)+8. 4. Find the extreme values of f(x)=x3-3x2-9x+5 for -25x56. 5. Find an antiderivative of the integrand and use Part 2 of the Fundamental Theorem to evaluate the definite integral. a) So(x2 - 1)dx b) Jz(sin x) dx c) Sext dx5. Use the change of variable technique to find an antiderivative in terms of x. a} Icosftix] dx b] [(3]: + 5:13 :11: c} felt\" [it 7". Find a} jx[_f:tan{u]du) b] '1 (I:ZMdE) E 8. Use integrals and the graphs of x] = 1 + x and gix} = 3 x to determine the area between the graphs of f and g for {i s x s 3. El. A robot has been programmed so that when it starts to move; its velocity.r after t seconds will be 35 feetj'second. {a} How far will the robot travel during its first 4 seconds of movement? {b} How far will the robot travel during its next 4 seconds of movement? {c} How man!\"r seconds before the robot is T29 feet from its starting place