Page 1 Math 151 copyright Joe Kahlig 09B 1 6 points Given m h2 7i and n h1 10i Find the vector projection of n onto m 2 6 points Find a vector equation of the line thru the points 1 7 and 3 12 3 15 points A pilot wishes to set a course so that his ground speed is northeast N45o E at 180 mph the wind is blowing in the direction of S30o E at 40 mph What course speed and bearing should the pilot set in order to achieve his desired ground speed Check the back of the page for more problems Page 2 Math 151 copyright Joe Kahlig 09B 4 16 points Find the derivatives for the following Assume that g x is a differentiable function DO NOT SIMPLIFY YOUR ANSWER 1 5 a f x x2 x2 4 5x b h x x4 3x 7 g x 5 9 points Find the equation of the tangent line at x 2 for the function f x x3 1 x 8 6 8 points Determine the values of x where the function is not continuous For each of these numbers state whether f is continuous from the right or from the left or neither 6 5 4 3 2 1 7 6 5 4 3 2 1 1 1 2 3 4 5 6 7 8 9 10 11 12 2 3 4 Check the back of the page for more problems Page 3 Math 151 copyright Joe Kahlig 09B 7 8 points Let r t t3 t 1 t2 9 Find a tangent vector s at the point 11 5 8 20 points Find the exact values of the following limits continued on the next page 2x2 7x 3 x 3 x2 9 a lim b x4 3x x 4 x2 lim x 2x2 1 c lim x 4x 1 Check the back of the page for more problems Page 4 Math 151 copyright Joe Kahlig 09B d lim x 2 1 4 2 x 2 x 4 9 6 points For what value s of c and m that will make the function f x be differentiable everywhere If this can not be done then explain why Fully justify your answers x2 for x 3 f x cx m for x 3 Check the back of the page for more problems Page 5 Math 151 copyright Joe Kahlig 09B 10 6 points Use the definition of the derivative to show that the derivative of f x x2 5x is f x 2x 5 Check the back of the page for more problems
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