MA 141 Midterm: MA 141 NCSU Practice3Sol
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Read all of the following information before starting the exam: complete each problem. Show all of your work clearly and in order and justify your answers, as partial credit will be given when appropriate and there may be no credit given for problems without supporting work. Circle or otherwise indicate your nal answers your nal answers. All answers should be completely simpli ed, unless otherwise stated. Use linear approximation to nd f (a + h) for f (x) = 1 cos x , a = . Solution: for linear approximation we rst need f (x) = sin x cos2 x , then we use the formula: f (a + h) f (a) + f (a)h = A rectangle with base on the x-axis has its upper vertices on the curve y = 3 x2. Solution: the area of the rectangle is given by a(x) = 2x(3 x2) and it reaches the maximum when a (x) = 6 6x2 = 0.
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