Questions from General Calculus

Q: Use graphs to determine which of the functions f (x)

Use graphs to determine which of the functions f (x) = 10x2 and g (x) = x3/10 is eventually larger (that is, larger when is very large).

Q: A variable star is one whose brightness alternately increases and decreases.

A variable star is one whose brightness alternately increases and decreases. For the most visible variable star, Delta Cephei, the time between periods of maximum brightness is 5.4 days, the average b...

Q: For what values of is it true that |sin x –

For what values of is it true that |sin x – x| < 0.1?

Q: Use the given graph of f to sketch the graph of y

Use the given graph of f to sketch the graph of y =1/f (x). Which features of are the most important in sketching y = 1/f (x)? Explain how they are used.

Q: In this exercise we consider the family of root functions f (

In this exercise we consider the family of root functions f (x) = n√x, where is a positive integer. (a). Graph the functions y = √x, y = 4√x and y = 6√x on the same screen using the viewing rectangle...

Q: The graph of is given. Match each equation with its graph

The graph of is given. Match each equation with its graph and give reasons for your choices. (a). y = f (x – 4) (b). y = f (x) – 3 (c). y = 1/3 f (x) (d). y = -...

Q: In this exercise we consider the family of functions f (x

In this exercise we consider the family of functions f (x) = 1/xn, where is a positive integer. (a). Graph the functions y = 1/x and y = 1/x3 on the same screen using the viewing rectangle [-3, 3] by...

Q: Graph the function f (x) = x4 + cx2 +

Graph the function f (x) = x4 + cx2 + x for several values of c. How does the graph change when changes?

Q: Graph the function f (x) = √1 + cx2

Graph the function f (x) = √1 + cx2 for various values of c. Describe how changing the value of c affects the graph.

Q: Find the domain of the function. h (x)

Find the domain of the function. h (x) = 1/4√x2 - 5x