Questions from General Calculus

Q: Sketch the region in the plane consisting of all points (x

Sketch the region in the plane consisting of all points (x, y) such that |x – y| + |x| - |y| < 2

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) = f0g + f0h?

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.

Q: Prove that 1 + 3 + 5 + … + (2n

Prove that 1 + 3 + 5 + … + (2n -1) = n2.

Q: (a). If f0 (x) = 1/ 2

(a). If f0 (x) = 1/ 2-x and fn+1 = f00 fn for n = 0, 1, 2, find an expression for fn (x) and use mathematical induction to prove it. (b). Graph f0, f1, f2, f3 on the same screen and describe the effec...

Q: (a). Eliminate the parameter to find a Cartesian equation of

(a). Eliminate the parameter to find a Cartesian equation of the curve. (b). Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases.

Q: Determine whether the statement is true or false. If it is

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. 1. If f is a function, then f (s + t) = f (s)...

Q: Find a formula for the inverse of the function. f

Find a formula for the inverse of the function. f (x) = 1 + √2 + 3x