Questions from General Calculus

Q: Evaluate limx→0 ((√1 + tan x) – (√

Evaluate limx→0 ((√1 + tan x) – (√1 + sin x)/x3)

Q: Find the limit. limx→∞ ex-x2

Find the limit. limx→∞ ex-x2

Q: Find the limit. limx→∞ (√x2 + 4x +

Find the limit. limx→∞ (√x2 + 4x + 1 - x)

Q: Find the limit. limx→1 (1/x

Find the limit. limx→1 (1/x – 1+ 1/x2 – 3x + 2)

Q: Use graphs to discover the asymptotes of the curve. Then prove

Use graphs to discover the asymptotes of the curve. Then prove what you have discovered. y = cos2x/x2

Q: Sketch the graph of an example of a function that satisfies all

Sketch the graph of an example of a function that satisfies all of the following conditions: f is continuous from the right at 3

Q: When you turn on a hot-water faucet, the temperature

When you turn on a hot-water faucet, the temperature T of the water depends on how long the water has been running. (a). Sketch a possible graph of T as a function of the time that has elapsed since t...

Q: If 2x – 1 < f (x) < x2 for

If 2x – 1 < f (x) < x2 for 0 < x < 3, find limx→1 f (x).

Q: Prove that limx→0 x2 cos (1/x2)

Prove that limx→0 x2 cos (1/x2) = 0.

Q: The displacement (in meters) of an object moving in a

The displacement (in meters) of an object moving in a straight line is given by s = 1 + 2t + 1/4t2, where is measured in seconds. (a). Find the average velocity over each time period. (b). Find the...