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### 2-F01-S01

Course: MATH 131, Fall 2008
School: UMass (Amherst)
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Word Count: 480

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131: Mathematics 2nd midterm, April 26, 2001 1) A squash ball is hit upwards so that its height in meters is given by h(t) = 5t - 10t2 , where t is the elapsed time in seconds. A. (10 pts) Find the velocity after 0.1 sec, 0.2 sec and 0.3 sec, respectively. B. (10 pts) When will the velocity be zero, and how high will the ball be then? C. (10 pts) At what time will the ball first hit the ground? With what velocity...

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131: Mathematics 2nd midterm, April 26, 2001 1) A squash ball is hit upwards so that its height in meters is given by h(t) = 5t - 10t2 , where t is the elapsed time in seconds. A. (10 pts) Find the velocity after 0.1 sec, 0.2 sec and 0.3 sec, respectively. B. (10 pts) When will the velocity be zero, and how high will the ball be then? C. (10 pts) At what time will the ball first hit the ground? With what velocity will it do so? 2) Let f(x) = e2x cos(x). A. (10 pts) Find the derivative f (x). B. (10 pts) Find the equation of the tangent line to the graph of y = f(x) at the point (0, 1). 3) The function f is given by f(t) = tet . A. (10 pts) Find its first and second derivatives. B. (10 pts) Give a formula for the n-th derivative f(n) (t). 4) (10 pts) Use logarithmic differentiation to find the derivative of g(x) = xln(x) , giving your answer in terms of x. 5) (10 pts) Find 6) A. (10 pts) Find the linearization of the function x at a = 16. B. (10 pts) Use differentials to approximate 16.5. dy dx when y is given implicitly by x2 y + xy3 = 1. 7) (20 pts) A (perfectly cubic) chunk of ice is melting so that its volume decreases at a rate of 15 cm3 /min. At what rate is the side of the cube changing when that side is 10cm long? Mathematics 131: 2nd midterm, Fall, 2001 1) A car position as a function of time is given by the formula = s f(t) = 2t3 - 9t2 + 12t where s is measured in feet and t is measured in seconds. A. (8 pts) What is the velocity of the car at time t? When is the car at rest? B. (8 pts) When is the car moving in the positive direction? In the negative direction? C. (8 pts) Find the total distance the car travels in the first 3 seconds. 2) Suppose a function is defined implicitly by (x2 + y2 )2 = x4 + 3. A. (8 pts) Find dy dx B. (6 pts) Find an equation of the tangent line to the curve at the point (1, 1). 3) (12 pts) The function f is given by f(x) = e6x A. Find its first and second derivatives B. Give a formula for the nth derivative f(n) (x). 4) (12 pts) Use logarithmic differentiation to find the derivative of f(x) = (x + 1)2 (x + 2)3 (x + 3)4 . Gives your answers in terms of x. f(x) 5) (12 pts) Let ...

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UMass (Amherst) - MATH - 131
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