Arrington Sample Math 0120 Sample Exam 1 Name (Print) PeopleSoft # . Signature Score . TA (Circle one) Instructions: 1. Clearly print your name and PeopleSoft number and sign your name in the space above. 2. There are 8 problems, each worth the specified number of points, for a total of 100 points. There is also an extra-credit problem worth up to 5 points. 3. Please work each problem in the space provided. Extra space is available on the back of each exam sheet. Clearly identify the problem for which the space is required when using the backs of sheets. 4. Show all calculations and display answers clearly. Unjustified answers will receive no credit. 5. Write neatly and legibly. Cross out any work that you do not wish to be considered for grading. 6 No calculators, headphones, tables, books, notes, or computers may be used. All derivatives are to be found by learned methods of calculus.Arrington Sample 1. (10 pts.) f(x) = 1x12x−− and g(x) = 1x+. (a) Find the domain of f(x) and express it in interval notation. (b) Find and simplify the composition f(g(x)). 2. (a) (5 pts) Find 2x8xlim32x−−→ (b) (5 pts.) Write the definition of the derivative of f(x). (c) (7 pts.) Use the definition to find the derivative of f(x) = x2.Arrington Sample 3. (32 pts.) Find the indicated derivatives of the following functions (you need not simplify, but you must use correct notation): (a) 21003x4x2x8)x(f4+π+−+−=−. ).x(fdxdFind22 Use Leibniz notation throughout. (b) . Find )x103x5)(x185x3()x(f −−−= ).x(f′ (c) Find )3xx2012x(dxd+−. (d) f(x) = 3)x11(−+ . Find ).x(f′ You may earn 5 points extra credit by finding )x(g′for g(x) = 439x2xx −−π+. .Arrington Sample 4. (a)(6 pts) The height of a projectile after t seconds is s(t) = -16t2 + 96t + 256 = -16(t + 2)(t – 8) feet, 0 ≤ t ≤ 8. What is the impact velocity of the projectile? (b)(6 pts.) After t hours a certain bicyclist is s(t) = 9t2 - 2t3 miles from his starting point, 0 ≤ t ≤ 4.5. Find his average acceleration between t=1 hour and t=3 hours. 5. (14 pts.) The cost function for a certain commodity is given by C(x) = 8x -123x+10 dollars, where x is the number of units produced. Find the marginal cost, the average cost and the marginal average cost. Estimate the cost of producing the 65-th unit.Arrington Sample 6. (7 pts.) xx)x(f += . Find the equation of the line tangent to the graph of y = f(x) at x = 1 in slope-intercept form. 7. (8 pts.) Give examples (no graphs) of (a) A function f that is defined at x = 3, but discontinuous at x = 3 because .existnotdoes)x(flim3x→ (b) A function g that is continuous at x = -1, but not differentiable at x = -1 because of a vertical tangent line at x =