ap-calc bc 2022

Which of the following statements about the power series above is true?

Based on the statements above, which of the following must be true?

Let $$f$$ be the function defined as shown. Which of the following statements about $$f$$ is false?

What are the first three nonzero terms of the Maclaurin series for the piecewise function defined as shown above?

Which of the following is a power series expansion for （含图）

The position of a particle moving in the $$xy$$-plane is given by the parametric functions $$x(t)$$ and $$y(t)$$, whose graphs are shown. What is the slope of the line tangent to the path of the particle at the point at which $$t = 2$$?

A slope field for the differential equation （含图） is shown. The point $$(2, -1)$$ is indicated in the figure. Let $$y = f(x)$$ be the solution to the differential equation with initial condition $$f(2) = -1$$. If $$f(3)$$ is approximated by using Euler's method with two steps of equal size starting at $$x = 2$$, which of the following statements is true?