Questions from General Calculus

Q: To determine the amount of water flowing down a certain 100-

To determine the amount of water flowing down a certain 100-yard-wide river, engineers need to know the area of a vertical cross section of the river. Measurements of the depth of the river were made...

Q: Upon takeoff, the velocity readings of a rocket noted every second

Upon takeoff, the velocity readings of a rocket noted every second for 10 seconds were 0, 30, 75, 115, 155, 200, 250, 300, 360, 420, and 490 feet per second. Use the trapezoidal rule to estimate the d...

Q: In a drive along a country road, the speedometer readings are

In a drive along a country road, the speedometer readings are recorded each minute during a 5-minute interval. Use the trapezoidal rule to estimate the distance traveled during the 5 minutes.

Q: Consider ∫0 2 f (x)dx, where f

Consider ∫0 2 f (x)dx, where f (x) = 1/12 x4 + 3x2. (a) Make a rough sketch of the graph of f ’’(x) for 0 ≤ x ≤ 2. (b) Find a number A such that | f ’’(x) | ≤ A for all x satisfying 0 ≤ x ≤ 2. (c) Obt...

Q: Consider ∫1 2 f (x)dx, where f

Consider ∫1 2 f (x)dx, where f (x) = 3 ln x. (a) Make a rough sketch of the graph of the fourth derivative of f (x) for 1 ≤ x ≤ 2. (b) Find a number A such that | f ’’ ’’ (x) | ≤ A for all x satisfyin...

Q: (a) Show that the area of the trapezoid in Fig

(a) Show that the area of the trapezoid in Fig. 13(a) is ½ (h + k) l. (b) Show that the area of the first trapezoid on the left in Fig. 13(b) is ½ [ f (a0) + f (a1)]Î...

Q: Approximate the value of ∫a b f (x)dx

Approximate the value of ∫a b f (x)dx, where f (x) ≥ 0, by dividing the interval a ≤ x ≤ b into four subintervals and constr...

Q: Determine the integrals by making appropriate substitutions. ∫ x4/(

Determine the integrals by making appropriate substitutions. ∫ x4/(x5 + 1) dx

Q: (a) Suppose that the graph of f (x)

(a) Suppose that the graph of f (x) is above the x-axis and concave down on the interval a0 ≤ x ≤ a1. Let x1 be the midpoint of this interval, let Δ...

Q: Subdivide the interval 0 ≤ t ≤ 22 into n subintervals of

Subdivide the interval 0 ≤ t ≤ 22 into n subintervals of length Δt = 22/n seconds. Let ti be a point in the ith subinterval. (a) Show that (R/60)Δt ≈ [number of liters of blood flowing past the monito...