Questions from General Calculus

Q: Sketch the graph of a function that satisfies the given conditions.

Sketch the graph of a function that satisfies the given conditions. f (0) = 0, f is continuous and even, f ‘(x) = 2x if 0 < x < 1, f ‘(x) = -1 if 1 < x < 3, f ‘(x) = 1 if x > 3

Q: Use the guidelines of Section 4.5 to sketch the curve

Use the guidelines of Section 4.5 to sketch the curve. y = (x – 2)e-x

Q: Use the guidelines of Section 4.5 to sketch the curve

Use the guidelines of Section 4.5 to sketch the curve. y = x + ln(x2 + 1)

Q: A spherical balloon is being inflated. Find the rate of increase

A spherical balloon is being inflated. Find the rate of increase of the surface area (S = 4πr2) with respect to the radius r when r is (a) 1 ft, (b) 2 ft, and (c) 3 ft. What conclusion can you make?...

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. Use graphs of f ‘ and f ’’ to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and infle...

Q: Produce graphs of f that reveal all the important aspects of the

Produce graphs of f that reveal all the important aspects of the curve. Use graphs of f ‘ and f ’’ to estimate the intervals of increase and decrease, extreme values, intervals of concavity, and infle...

Q: (a) Graph the function f (x) = 1

(a) Graph the function f (x) = 1/(1 + e1/x). (b) Explain the shape of the graph by computing the limits of f (x) as x approaches ∞, -∞, 0+, and 0-. (c) Use the graph of f to estimate the coordinates o...

Q: (a) Find the average rate of change of the area

(a) Find the average rate of change of the area of a circle with respect to its radius r as r changes from (i) 2 to 3 (ii) 2 to 2.5 (iii) 2 to 2.1 (b) Find the instantaneous rate of change when r = 2....

Q: Investigate the family of functions f (x) = ln(

Investigate the family of functions f (x) = ln(sin x + C). What features do the members of this family have in common? How do they differ? For which values of C is f continuous on (-∞, ∞)? For which v...

Q: Show that the equation 3x + 2 cos x + 5 =

Show that the equation 3x + 2 cos x + 5 = 0 has exactly one real root.