Questions from General Calculus

Q: Match the graphs of the parametric equations x = f (t

Match the graphs of the parametric equations x = f (t) and y = g (t) in (a)–(d) with the parametric curves labeled I–IV. Give reasons for your choices.

Q: Solve each equation for x. (a). ln (

Solve each equation for x. (a). ln (x2 – 1) = 3 (b). e2x – 3ex + 2 = 0

Q: Solve each equation for x. (a). 2x-

Solve each equation for x. (a). 2x-5 = 3 (b). ln x + ln (x – 1) = 1

Q: Solve each equation for x. (a). ln (

Solve each equation for x. (a). ln (ln x) = 1 (b). eax = Cebx, where a ≠ b

Q: Solve each inequality for x. (a). ex >

Solve each inequality for x. (a). ex > 10 (b). ln x > -1

Q: Solve each inequality for x. (a). 2 <

Solve each inequality for x. (a). 2 < ln x < 9 (b). e2-3x > 4

Q: Find (a) the domain of f and (b)

Find (a) the domain of f and (b) f-1 and its domain. f (x) = √3 - e2x

Q: Find (a) the domain of f and (b)

Find (a) the domain of f and (b) f-1 and its domain. f (x) = ln (2 + ln x)

Q: Find the domain of each function. (a). g

Find the domain of each function. (a). g (t) = sin (e-t) (b). g (t) = √1 - 2t

Q: Find the exponential function f (x) = Cax whose graph

Find the exponential function f (x) = Cax whose graph is given.