Questions from General Calculus

Q: f (x) = x - 2 cos x, -

f (x) = x - 2 cos x, -2 < x < 0 (a). Use a graph to estimate the absolute maximum and minimum values of the function to two decimal places. (b). Use calculus to find the exact maximum and minimum valu...

Q: Between 00C and 300C, the volume V (in cubic centimeters

Between 00C and 300C, the volume V (in cubic centimeters) of 1 kg of water at a temperature T is given approximately by the formula V = 999.87 - 0.06426T + 0.0085043T2 - 0.0000679T3 Find the temperatu...

Q: h (x) = (x + 1)5 -

h (x) = (x + 1)5 - 5x - 2 (a). Find the intervals of increase or decrease. (b). Find the local maximum and minimum values. (c). Find the intervals of concavity and the inflection points. (d). Use the...

Q: f (x) = ln (x4 + 27)

f (x) = ln (x4 + 27) (a). Find the intervals of increase or decrease. (b). Find the local maximum and minimum values. (c). Find the intervals of concavity and the inflection points. (d). Use the infor...

Q: (a). Show that ex > 1 + x for x

(a). Show that ex > 1 + x for x > 0. (b). Deduce that ex > 1 + x + 1/2x2 for x > 0. (c). Use mathematical induction to prove that for x > 0 and any positive integer n,

Q: f (x) = 2 + 2x2 - x4 (

f (x) = 2 + 2x2 - x4 (a). Find the intervals of increase or decrease. (b). Find the local maximum and minimum values. (c). Find the intervals of concavity and the inflection points. (d). Use the infor...

Q: Suppose that f (0) = -3 and f'(

Suppose that f (0) = -3 and f'(x) < 5 for all values of x. The inequality gives a restriction on the rate of growth of f, which then imposes a restriction on the possible values of f. Use the Mean Val...

Q: Suppose that 3 < f'(x) < 5 for all

Suppose that 3 < f'(x) < 5 for all values of x. Show that 18 < f (8) – f (2) < 30.

Q: Two runners start a race at the same time and finish in

Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed. [Hint: Consider f (t) = g (t) – h (t), where and are the position funct...

Q: At 2:00 PM a car’s speedometer reads 30 mi/

At 2:00 PM a car’s speedometer reads 30 mi/h. At 2:10 PM it reads 50 mi/h. Show that at some time between 2:00 and 2:10 the acceleration is exactly 120 mi/h2.