Questions from General Calculus

Q: If oil leaks from a tank at a rate r (t

If oil leaks from a tank at a rate r (t) of gallons per minute at time f020 r (t) dt, what does represent?

Q: If f' is continuous on [0, ∞] and limx→∞

If f' is continuous on [0, ∞] and limx→∞f (x) = 0, show that f∞0f' (x) dx = -f (0).

Q: The figure shows two regions in the first quadrant: A (

The figure shows two regions in the first quadrant: A (t) is the area under the curve y = sin (x2) from 0 to t, and B (t) is the area of the triangle with vertices O, P, and (t, 0). Find limtâ&#...

Q: (a). Find the vertical and horizontal asymptotes, if any

(a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the...

Q: (a). Find the vertical and horizontal asymptotes, if any

(a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the...

Q: (a). Find the vertical and horizontal asymptotes, if any

(a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the...

Q: (a). Find the vertical and horizontal asymptotes, if any

(a). Find the vertical and horizontal asymptotes, if any. (b). Find the intervals of increase or decrease. (c). Find the local maximum and minimum values. (d). Find the intervals of concavity and the...

Q: Graph f (x) = e-1/x2 in

Graph f (x) = e-1/x2 in a viewing rectangle that shows all the main aspects of this function. Estimate the inflection points. Then use calculus to find them exactly.

Q: Let R be the region in the first quadrant bounded by the

Let R be the region in the first quadrant bounded by the curves y = x3 and y = 2x – x2. Calculate the following quantities. (a). The area of R (b). The volume obtained by rotating R about the x-axis (...

Q: Find the local and absolute extreme values of the function on the

Find the local and absolute extreme values of the function on the given interval.