Questions and Worked options For AP Calculus BC 2017

AP Calculus BC 2017 cost-free Response concerns - Complete document (pdf)

AP Calculus BC 2017 cost-free Response question 1

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A tank has a elevation of 10 feet. The area that the horizontal cross section of the tank at elevation h feet is provided by the duty A, whereby A(h) is measure up in square feet. The role A is consistent and decreases together h increases. Selected values for A(h) are offered in the table above.

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(a) use a left Riemann amount with the three subintervals indicated by the data in the table to almost right the volume of the tank. Suggest units that measure.(b) walk the approximation in part (a) overestimate or underestimate the volume that the tank? define your reasoning.(c) The area, in square feet, the the horizontal cross ar at height h feet is modeled by the function f given by

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based upon this model, uncover the volume that the tank. Indicate units that measure.(d) Water is pumped right into the tank. As soon as the elevation of the water is 5 feet, the height is enhancing at the rate of 0.26 foot per minute. Making use of the design from component (c), uncover the rate at i m sorry the volume of water is changing with respect come time once the elevation of the water is 5 feet. Show units that measure.

AP Calculus BC 2017 free Response concern 2

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The figure over shows the polar curves r = f(θ) = 1 + sinθcos(2θ) and r = g(θ) = 2cosθ because that 0 ≤ θ ≤ π/2. Permit R be the an ar in the an initial quadrant bounded through the curve r = f(θ) and the x-axis. Permit S be the region in the an initial quadrant bounded by the curve r = f (&theta), the curve r = g(θ), and also the x-axis.

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(a) find the area the R.(b) The beam θ = k, whereby 0 (c) because that each θ, 0 ≤ θ ≤ π/2, allow w(θ) be the distance between the points through polar coordinates (f(θ),θ) and (g(θ),θ). Write an expression because that w(θ). Discover wA, the typical value of w(θ) end the interval 0 ≤ θ ≤ π/2.(d) utilizing the information from component (c), discover the worth of θ because that which w(θ) = wA. Is the role w(θ) boosting or decreasing at that worth of θ ? offer a factor for your answer.


AP Calculus BC 2017 totally free Response inquiry 3

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The function f is differentiable top top the close up door interval <−6, 5> and satisfies f(−2) = 7. The graph that f", the derivative that f, consists of a semicircle and three line segments, as displayed in the number above.(a) find the values of f(−6) and f(5).(b) top top what intervals is f increasing? Justify your answer.(c) find the pure minimum worth of f on the closed interval <−6, 5>. Justify her answer.(d) for each of f"(-5) and f “(3), uncover the value or describe why that does no exist.

AP Calculus BC 2017 totally free Response question 4

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AP Calculus BC 2017 totally free Response question 5

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AP Calculus BC 2017 free Response concern 6

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