Stanford_MT_2020_Calculus.pdf - SMT 2019 Calculus Test...

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SMT 2019 Calculus Test March 2, 2019 Comment: Version 1.3 Time limit: 50 minutes. Instructions: This test contains 10 short answer questions. All answers must be expressed in simplest form unless specified otherwise. Only answers written inside the boxes on the answer sheet will be considered for grading. No calculators. DT02 1. If f ( x ) = nx , g ( x ) = e 2 x , and h ( x ) = g ( f ( x )), find n such that h 0 (0) = 100. KW36 2. Farmer Joe will plant carrots to cover a rectangle in the first quadrant with a vertex at the origin and sides parallel to the x and y axes. However, he can not grow carrots on his neighbor’s land. If the border between his and his neighbor’s land is along the curve y = - ln(2 x ), what is the maximum area of carrotland Farmer Joe can create? KW40 3. For all θ from 0 to 2 π , Annie draws a line segment of length θ from the origin in the direction of θ radians. What is the area of the spiral swept out by the union of these line segments?

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