Questions from General Calculus

Q: The graph of a function is shown in the figure. Make

The graph of a function is shown in the figure. Make a rough sketch of an antiderivative F, given that F(0) = 1.

Q: Write the composite function in the form f ( g(x

Write the composite function in the form f ( g(x) ). [Identify the inner function u = g(x) and the outer function y = f (u).] Then find the derivative dy / dx. y = sin cot x

Q: Differentiate the function. Y = log2 (x log5 x

Differentiate the function. Y = log2 (x log5 x)

Q: The graph of the velocity function of a particle is shown in

The graph of the velocity function of a particle is shown in the figure. Sketch the graph of a position function.

Q: The graph of f ‘ is shown in the figure. Sketch

The graph of f ‘ is shown in the figure. Sketch the graph of f if f is continuous and f (0) = -1.

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. v(t) = sin t - cos t, s(0) = 0

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. a(t) = 2t + 1, s(0) −= 3, v(0) = -2

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. a(t) = 3 cos t - 2 sin t, s(0) = 0, v(0) = 4

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. a(t) = 10 sin t + 3 cos t, s(0) = 0, s(2π) = 12

Q: A particle is moving with the given data. Find the position

A particle is moving with the given data. Find the position of the particle. a(t) = t2 - 4t + 6, s(0) = 0, s(1) = 20