Questions from General Calculus

Q: Prove that /

Prove that

Q: Prove that / √x = √a if a > 0

Prove that / √x = √a if a > 0.

Q: If H is the Heaviside function defined in Example 2.2

If H is the Heaviside function defined in Example 2.2.6, prove, using Definition 2, that limt→0 H(t) does not exist.

Q: If the function f is defined by /

If the function f is defined by prove that limx→0 f(x) does not exist.

Q: By comparing Definitions 2, 3, and 4, prove Theorem

By comparing Definitions 2, 3, and 4, prove Theorem 2.3.1.

Q: How close to -3 do we have to take x so

How close to -3 do we have to take x so that

Q: Prove, using Definition 6, that /

Prove, using Definition 6, that

Q: Prove that / ln x = -∞.

Prove that / ln x = -∞.

Q: Suppose that limx→a f(x) = ∞ and

Suppose that limx→a f(x) = ∞ and limx→a g(x) = c, where c is a real number. Prove each statement.

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

Sketch the graph of an example of a function f that satisfies all of the given conditions.