ap calc bc 2021_在线真题试卷与模拟练习_ap calc bc 2021

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（含图）

The first and second derivatives of a function $$f$$ have the properties given in the table above. Which of the following could be the graph of $$f$$?

If （含图）, then $$f'(x) =$$

A particle moves in the $$xy$$-plane so that its position at time $$t > 0$$ is given by $$x(t) = 2\ln t$$ and $$y(t) = \frac{4}{t + 1}$$. What is the speed of the particle when $$t = 1$$?

If $$\cos b = \frac{1}{3}$$ for a constant $$b$$, then $$\sum_{n = 0}^{\infty}(\sin^2 b)^n =$$

（含图）

Let $$f$$ be a function with derivatives of all orders. If $$P_3(x)$$ is the third-degree Taylor polynomial for $$f$$ about $$x = 0$$, which of the following statements about $$P_3(x)$$ must be true?

（含图） is

（含图）

Let $$g$$ be the function given above. What is the average rate of change of $$g$$ on the closed interval $$[1,5]$$?

Let $$f$$ be a differentiable function with $$f(2) = 3$$ and $$f'(2) = \frac{1}{2}$$. Using the line tangent to the graph of $$f$$ at $$x = 2$$ as a local linear approximation for $$f$$, what is the estimate for $$f(1.8)$$?

Let $$g$$ be a function such that （含图）

Which of the following could be the graph of $$g$$?

Which of the following is the solution to the differential equation （含图） with the initial condition （含图）

（含图）

If $$\frac{dy}{dx} = 16\sin^3x\cos x$$ and $$y = 16$$ when $$x = \frac{\pi}{2}$$, what is the value of $$y$$ when $$x = \frac{\pi}{6}$$?

Consider the series （含图）

Which of the following statements is true?

（含图）

Let be $$R$$ the region in the first quadrant that is bounded by the polar curve （含图） as shown in the figure above. What is the area of $$R$$?

Consider the series （含图）

Which of the following statements is true?

Let $$f$$ be a continuous function such that $$f(x) = f(-x)$$ for all $$x$$.

If （含图）what is the value of （含图）

What are all values of $$x$$ for which the series （含图） converges?

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