Questions from General Calculus

Q: The figure shows a horizontal line y = c intersecting the curve

The figure shows a horizontal line y = c intersecting the curve y = 8x – 27x3. Find the number c such that the areas of the shaded regions are equal.

Q: Evaluate limx→∞ (1/√n √n + 1,

Evaluate limx→∞ (1/√n √n + 1, + 1/√n √n + 2, + . . . + 1/√n √n + n.

Q: One of the problems posed by the Marquis de l’Hospital in his

One of the problems posed by the Marquis de l’Hospital in his calculus textbook Analyse des Infiniment Petits concerns a pulley that is attached to the ceiling of a room at a point C...

Q: Find d2/dx2 fx0(fsint1 √1 + u4,

Find d2/dx2 fx0(fsint1 √1 + u4, du) dt.

Q: Evaluate the integral. f-23 (x2 – 3

Evaluate the integral. f-23 (x2 – 3) dx

Q: A man initially standing at the point O walks along a pier

A man initially standing at the point O walks along a pier pulling a rowboat by a rope of length L. The man keeps the rope straight and taut. The path followed by the boat is a curve called a tractrix...

Q: Show that |sin x – cos x | < √2

Show that |sin x – cos x | < √2 for all x.

Q: If f40e(x-2)4 dx = k,

If f40e(x-2)4 dx = k, find the value of f40xe(x-2)4 dx.

Q: If x sin πx = fx20f (t) dt, where

If x sin πx = fx20f (t) dt, where f is a continuous function, find f (4).

Q: If f (x) = fx0x2 sin (t2) dt

If f (x) = fx0x2 sin (t2) dt, find f'(x).