Questions from General Calculus

Q: The notation max{a, b, ...} means the largest

The notation max{a, b, ...} means the largest of the numbers a, b, ... . Sketch the graph of each function. a. f(x) = max{x, 1/x} b. f(x) = max{sin x, cos x} c. f(x) = max{x2, 2 + x, 2 - x}

Q: Sketch the region in the plane defined by each of the following

Sketch the region in the plane defined by each of the following equations or inequalities. a. max{x, 2y} = 1 b. -1 ≤ max{x, 2y} ≤ 1 c. max{x, y2} = 1

Q: Evaluate (log23)(log34)(log45)∙∙∙(log3132).

Evaluate (log23)(log34)(log45)∙∙∙(log3132).

Q: a. Show that the function f(x) = ln

a. Show that the function f(x) = ln(x + x2 + 1 ) is an odd function. b. Find the inverse function of f.

Q: Solve the inequality ln(x2 - 2x – 2) ≤

Solve the inequality ln(x2 - 2x – 2) ≤ 0.

Q: Find the domain of the function. /

Find the domain of the function.

Q: Use indirect reasoning to prove that log25 is an irrational number.

Use indirect reasoning to prove that log25 is an irrational number.

Q: A driver sets out on a journey. For the first half

A driver sets out on a journey. For the first half of the distance she drives at the leisurely pace of 30 mi/h; she drives the second half at 60 mi/h. What is her average speed on this trip?

Q: Is it true that f 0 (g + h) =

Is it true that f 0 (g + h) = f 0 g + f 0 h?

Q: Prove that if n is a positive integer, then 7n -

Prove that if n is a positive integer, then 7n - 1 is divisible by 6.