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graph. derivative. ". (x(x) +4) dx [(28(0)-x) 4x 7. Answer all the following question ". [ (ar - _ + sin(3) dx etedx = + C. i. Compute [ (antanox) Compute lim ) (33+ +. #) ili. Use three midpoint approximations [()dx = 2. Compute the following: li. Use three left endpoint approximations i. Use three right endpoint approximations sin(x) 1. The graph of a continuous function fis given below. interval [-2.41. Is it possible for fundx cos (2 + 5.!) . " ). Note: the input of cosine is ( 2 + ! ) b. lim (+ ed arctan(x) b. A student claimed that (e" sin(x) dx = ze" sin(x) - -e" cos(x) + C. Verify whether or not this is 2. Compute the derivative of the following functions correct. Tell the student how they can check their work on their own without the using any technology. . Let p be the position of some particle. Its velocity is given by the formula v(!) = 5: - 12, where v is a. f(x) = x cos(3x) measured in meters per se cured in seconds. b. f(x) = arctan(x) - In(10)In(x) a. Find a formula for the position iven that the initial position of the particle is p(0) = 5 meters 3. Compute x3 dx by using the definition of the definite integral as a LIMIT of Riemann Sums. Do not use Find a formula for the acceleration of the particle at time t. . Find the displacement of the particle over the time interval [0.8]. anti-derivative formulas or fundamental theorem of calculus. d. Find the total distance traveled by the particle over the time interval [0,8]. Compute the following. Then check your work by taking the appropriate derivative to receive full credit. 8. The graph of a continuous function fis given: a. Approximate the area under the curve y = f(x) from x = 2 to x = 6 using two right endpoint Riemann a. 4 sec?(x) + In(3) + -2 4 1 dx sums. In addition, draw your approximations. Approximate the area under the curve y = f(x) from x = 2 to b. 5x3 cos(x] ) dx x = 6 using two left endpoint Riemann sums. In addition, draw your approximations. 5. Compute the following. xet'+dx b. ( 5 " - 14 + 2) dx