Questions from General Calculus

Q: Figure 5 shows the graphs of several functions f (x)

Figure 5 shows the graphs of several functions f (x) for which f ‘(x) = 1/3. Find the expression for the function f (x) whose graph passes through (6, 3). Figure 5:

Q: Which of the following is ∫ln x dx? (

Which of the following is ∫ln x dx? (a) 1/x + C (b) x * ln x - x + C (c) ½ * (ln x)2 + C

Q: Find all antiderivatives of each following function: f (x

Find all antiderivatives of each following function: f (x) = 3

Q: Which of the following is ∫x√(x + 1)

Which of the following is ∫x√(x + 1) dx? (a) 2/5 (x + 1)5/2 – 2/3 (x + 1)3/2 + C (b) ½ x2 * 2/3 (x + 1)3/2 + C

Q: Figure 6 contains the graph of a function F (x).

Figure 6 contains the graph of a function F (x). On the same coordinate system, draw the graph of the function G(x) having the properties G (0) = 0 and G ’(x) = F ‘...

Q: Figure 7 contains an antiderivative of the function f (x).

Figure 7 contains an antiderivative of the function f (x). Draw the graph of another antiderivative of f (x). Figure 7:

Q: The function g(x) in Fig. 8 resulted from

The function g(x) in Fig. 8 resulted from shifting the graph of f (x) up 3 units. If f ‘(5) = 1/4 , what is g(5)? Figure 8:

Q: The function g(x) in Fig. 9 resulted from

The function g(x) in Fig. 9 resulted from shifting the graph of f (x) up 2 units. What is the derivative of h(x) = g(x) - f (x)? Figure 9:

Q: A ball is thrown upward from a height of 256 feet above

A ball is thrown upward from a height of 256 feet above the ground, with an initial velocity of 96 feet per second. From physics it is known that the velocity at time t is y(t) = 96 - 32t feet per sec...

Q: A rock is dropped from the top of a 400-foot

A rock is dropped from the top of a 400-foot cliff. Its velocity at time t seconds is y(t) = -32t feet per second. (a) Find s(t), the height of the rock above the ground at time t. (b) How long will t...