#42 PRACTICE TEST 4Bridges Name ____________________Math 124 Updated November 2010#42 PRACTICE TEST 4(4.6 – 7.1)PART 1 – YOU MAY NOT USE A CALCULATOR ON THESE PROBLEMS.1. Find each of these indefinite integrals. Simplify answers.(a)∫(0 . 4 x5−1x+1cos2x)dx(b)∫6 cos(2ω )sin (2ω )+3dω2. Find each of these definite integrals. Give exact and simplest answers.(a)∫13x(1+x2)2dx1(b)∫1e√x +1√xdx3. Find this derivative: ddx∫2√xarcsin(t ) dt4. Consider the function k ( x )=xex2.(a) Find the exact area under the graph of k(x ) between x = 0 and x = 2. (b) Find the average value of k(x) between x = 0 and x = 2.2PART 2 – YOU MAY USE A CALCULATOR ON THESE PROBLEMS.5. An object travels horizontally at constant acceleration. Initially traveling at 23 meters per second, it accelerates to 76 meters per second in 8 seconds.(a) Write the equation for the acceleration of the object as a function of time.(b) Write the equation for the velocity of the object as a function of time.(c) Write the equation for the distance traveled by the object as a function of time. (d) To the nearest meter, find the total distance traveled by the object during these 8 seconds. 6. Consider K ( x )=∫3x−1ew2dw(a) When is K ( x ) increasing and when is it decreasing? Explain.(b) When is K ( x ) concave up and when is it concave down? Explain(c) When are the values of K ( x ) positive and when are they negative? Explain(d) Sketch K ( x ) as accurately and as neatly as possible. Label key points on your graph.3yx7. Let f(x) be the derivative of F(x). Below is the graph of f(x). (a) Complete this chart for F(x) given that F(0) = 10.x -2 0 2 4 6 7 8 10F(x) 10(b) Neatly graph F(x) below. Be sure to label units on the axes. Draw your graph with a straight line if it should be a straight line and as a curve if it should be a curve.8. A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding by 0.1 meters/minute and its thickness is 0.02 meter. At that moment the circular slick has the same thickness everywhere, and the volume of oil spilled remains fixed. How fast is the thickness to the slick decreasing?4-4 -2 0 2 4 6 8 10 12-15-10-5051015f(x)xy9. Two little problems:(a) If possible, use L’Hopital’s Rule to find this limit: limx→ 1x2∙ ln(x )1−x2 . Be sure to show all work.(b) Use L’Hopital’s Rule to show that √x❑dominates ln(x ). Be sure to show all
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