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# Test1A - 4 Use the following table of times and distances...

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MA141-001 Test 1A February 2, 2010 Amanda Smith North Carolina State University Department of Mathematics Please put all work in the stamped blue book that has been provided. Nothing on this test sheet will be graded. Please put one problem on each page; you are allowed to use the back of the sheet as a new page. No calculators, formula sheets, or other aids are permitted. Please show all of your work. Simplify all solutions completely and clearly indicate your answers. Write your name on both the blue book and this test sheet. 1. [6 pts. ] Graph and write the equation for y - 1 ( x ) given y ( x ) = 5 x . Label at least one point. 2. Find the inverse of each of the following: (a) [6 pts. ] P ( x ) = x 4 + 32 (b) [6 pts. ] y = 2 - e x 5 - e x 3. Given the parametric equations: x = 5 cos ( t ) y = 5 sin ( t ) 0 t 3 π (a) [6 pts. ] Eliminate the parameter. (b) [6 pts. ] Sketch the parametric curve. Use arrows to indicate the direction the curve is traced as the parameter increases. (c) [6 pts. ] Find the initial and terminal points.

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Unformatted text preview: 4. Use the following table of times and distances at time t to do the following problems. Time (hours) 1 2 3 4 Distance (miles) 13 20 27 35 (a) [6 pts. ] Find the average velocity over [0 , 4]. (b) [6 pts. ] Approximate the instananeous velocity at t = 2. 5. Find the following limits if they exist. (a) [6 pts. ] lim t → √ t 2 + 4-2 t 2 ! (b) [6 pts. ] lim x → 3 ± x 2-x-6 x-3 ² (c) [6 pts. ] lim x → ± 1 x 2 ² MA141-001 Test 1A February 2, 2010 Amanda Smith 6. Use the graph of g ( x ) below to do the following problems. (a) [6 pts. ] Find lim x →-4-g ( x ). (b) [6 pts. ] Find lim x →-4 + g ( x ). (c) [6 pts. ] Find lim x → g ( x ). (d) [8 pts. ] Is g ( x ) continuous at x = 0? Explain why or why not. (e) [8 pts. ] Is g ( x ) continuous at x =-4? Explain why or why not. Bonus : [2 pts. ] Geometrically speaking, how is a cycloid contructed?...
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Test1A - 4 Use the following table of times and distances...

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