Questions from General Calculus

Q: a. Estimate the value of the limit limx→0 (

a. Estimate the value of the limit limx→0 (1 + x)1/x to five decimal places. Does this number look familiar? b. Illustrate part (a) by graphing the function y = (1 + x)1/x.

Q: Find the limit. /

Find the limit.

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: 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 = x2 + x + 1 - x2 − x

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: Prove the statement using the precise definition of a limit.

Prove the statement using the precise definition of a limit.

Q: Prove the statement using the precise definition of a limit.

Prove the statement using the precise definition of a limit.

Q: Prove the statement using the precise definition of a limit.

Prove the statement using the precise definition of a limit.

Q: Prove the statement using the precise definition of a limit.

Prove the statement using the precise definition of a limit.