Math 151-copyright Joe Kahlig, 09B Page 11. (6 points) Given m = h2, 7i a nd n = h1, 10i. Find the vector projection of n onto m2. (6 points) Find a vector e quation 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(N45oE) at 180 mph. thewind is blowing in the dire ction of S30oE at 40 mph. What course (speed and bearing) should the pilotset in order to achieve his desired ground speed?Check the back of the page for more problems.Math 151-copyright Joe Kahlig, 09B Page 24. (16 points) Find the derivatives for the following. Assume that g(x) is a differentiable function. DO NOTSIMPLIFY YOUR ANSWER.(a) f(x) = x25√x2+15x4(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+ 1x + 8.6. (8 points) Determine the values of x where the function is not continuous. For each of these numbersstate whether f is continuous from the right, or from the left, or neither.−1 1 3 4 5 6 7 81235462−3−4−4−5−6−7 −3−1−2 9 10 1211−2Check the back of the page for more problems.Math 151-copyright Joe Kahlig, 09B Page 37. (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)(a) limx→32x2− 7x + 3x2− 9=(b) limx→−∞x4+ 3x4 − x2=(c) limx→−∞x +√2x2+ 14x + 1=Check the back of the page for more problems.Math 151-copyright Joe Kahlig, 09B Page 4(d) limx→21x − 2−4x2− 4=9. (6 points) For what value(s) of c and m that will make the function f (x) be differentiable everywhere. Ifthis can not be done, then explain why. Fully justify your answers.f(x) =x2for x < 3cx + m for x ≥ 3Check the back of the page for more problems.Math 151-copyright Joe Kahlig, 09B Page 510. (6 points) Use the definition of the derivative to show that the derivative of f(x) = x2+ 5x is f′(x) = 2 x + 5.Check the back of the page for more
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