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Pitt MATH 0220 - MATH 0220 EXAM

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MATH 0220 EXAM II NAME1. Differentiate each of the following. It’s not necessary to simplify your answers.(a) f(x) =3√1 + x + 3x2(b) s(t) = arctan (2t)(c) y =tan x1 + cos x(d) g(x) = ln (x + e−3x)(e) f(x) =5(x2− 4)3(f) y = xcos x2. (a) Determine the equation of the tangent line to the curve:x2sin y + 3x + 2y = 6 at the point (2, 0).(b) Use your answer in part (a) to approximate y when x = 2.43. Find the point(s) on the parabola y = x2that is (are) closest to the point (0, 1).4. A lighthouse is 100 meters from a straight shoreline. The light turns at a rate of10 revolutions per minute (20π radians/minute), and shines a moving spot of lightalong the shore. How fast is the spo t of light moving when it’s 100 meters f r om thepoint on t he shore which is nearest the lighthouse? Be sure to include units in youranswer.5. Use Newton’s Method once to estimate the solution to the equation x = e−x. (Notethat the plot of f (x) = x − e−xis shown below.)0 1x6. Determine each of the following limits. Show your work.(a) limx→0sin xex− 1(b) limx→0ex− 1cos x(c) limx→0(1 +


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Pitt MATH 0220 - MATH 0220 EXAM

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