Questions from General Calculus

Q: Use continuity to evaluate the limit. limx→3 (

Use continuity to evaluate the limit. limx→3 (x3 – 3x + 1)-3

Q: Prove that limx→0 x4 cos 2/x = 0

Prove that limx→0 x4 cos 2/x = 0.

Q: Show that f is continuous on (-∞, ∞). /

Show that f is continuous on (-∞, ∞).

Q: Find the limit, if it exists. If the limit does

Find the limit, if it exists. If the limit does not exist, explain why.

Q: The graphs of f and t are given. Use them to

The graphs of f and t are given. Use them to evaluate each limit, if it exists. If the limit does not exist, explain why.

Q: The gravitational force exerted by the earth on a unit mass at

The gravitational force exerted by the earth on a unit mass at a distance r from the center of the planet is where M is the mass of the earth, R is its radius, and G is the gravitational constant. Is...

Q: Find the limit, if it exists. If the limit does

Find the limit, if it exists. If the limit does not exist, explain why.

Q: Find the limit, if it exists. If the limit does

Find the limit, if it exists. If the limit does not exist, explain why.

Q: Let / (a). Evaluate each of

Let (a). Evaluate each of the following, if it exists. (b) Sketch the graph of g.

Q: Suppose that a function f is continuous on [0, 1

Suppose that a function f is continuous on [0, 1] except at 0.25 and that f (0) = 1 and f (1) = 3. Let N = 2. Sketch two possible graphs of f, one showing that f might not satisfy the conclusion of th...