Page 1 Math 151 copyright Joe Kahlig 09B 1 18 points Find a y dy for the following dx 4 x2 7x b y 5 x2 y 3 5x c y tan 5x2 csc x 2 4 points Evaluate 3 2 log3 4 3 3 6 points Find the equation of the tangent line to y sec x 2 cos x at x 3 Check the back of the page for more problems Page 2 Math 151 copyright Joe Kahlig 09B 4 12 points Compute these limits Give exact values of these limits 1 a lim 2 x 3 x 3 b lim x 0 10 sin 5x tan 6x 3e2x 4e 2x x 5e 2x 7ex c lim 5 5 points Find the inverse of the function y 5 2x3 Check the back of the page for more problems Page 3 Math 151 copyright Joe Kahlig 09B 6 8 points a Find the linearization L x of the function f x b Use the answer in part a to estimate 3 x 60 at a 4 3 70 7 10 points Solve the following problems for x Give exact answers when possible a 7ex 8 35 b log2 1 2x log2 4x 2 Check the back of the page for more problems Page 4 Math 151 copyright Joe Kahlig 09B 8 6 points Find f x for f x e3x 2 9 12 points The curve is defined by x 2t3 3t2 12t y t2 t 1 a Find all the values of t for which the tangent line is horizontal b Find all the values of t for which the tangent line is vertical c Find dy evaluated at the point 13 1 dx Check the back of the page for more problems Page 5 Math 151 copyright Joe Kahlig 09B 10 5 points f x 4 x ex 2 is a one to one function with inverse g x Compute g 7 11 5 points The circumference of a sphere the length of its equatorial circle was measured to be 20cm with a possible error of 1 cm Estimate a maximum error in the calculated volume of the sphere using 4 differentials Recall that the volume of a sphere is V r3 and the circumference of a circle is C 2 r 3 Here r is the radius 12 9 points A trough is 10 feet long and its ends have the shape of isosceles triangles that are 4 feet across the top and have a height of 1 foot If the height of the water is decreasing at a rate of 0 15 ft min when the water is 6 inches deep find the rate of change of the volume of the tank at this time Check the back of the page for more problems
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