Questions from General Calculus

Q: Find the volume of the described solid S. The base

Find the volume of the described solid S. The base of S is the same base as in Exercise 42, but crosssections perpendicular to the x-axis are isosceles triangles with height equal to the base. Exerc...

Q: The base of S is a circular disk with radius r.

The base of S is a circular disk with radius r. Parallel crosssections perpendicular to the base are isosceles triangles with height h and unequal side in the base. (a). Set up an integral for the vol...

Q: Use the Comparison Theorem to determine whether the integral is convergent or

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

Q: Use the Comparison Theorem to determine whether the integral is convergent or

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

Q: (a). Cavalieri’s Principle states that if a family of parallel

(a). Cavalieri’s Principle states that if a family of parallel planes gives equal cross-sectional areas for two solids S1 and S2, then the volumes of S1 and S2 are equal. Prove this...

Q: Find the volume common to two circular cylinders, each with radius

Find the volume common to two circular cylinders, each with radius r, if the axes of the cylinders intersect at right angles.

Q: The integral f∞01/√x(1 + x)

The integral f∞01/√x(1 + x) is improper for two reasons: The interval [0, ∞] is infinite and the integrand has an infinite discontinuity at 0. Eva...

Q: Find the values of p for which the integral converges and evaluate

Find the values of p for which the integral converges and evaluate the integral for those values of p.

Q: f (x) = (x – 3)2,

f (x) = (x – 3)2, [2, 5] (a). Find the average value of f on the given interval. (b). Find such that fave = f (c). (c). Sketch the graph of f and a rectangle whose area is the same as the area under...

Q: Two cars, A and B, start side by side and

Two cars, A and B, start side by side and accelerate from rest. The figure shows the graphs of their velocity functions. (a). Which car is ahead after one minute? Explain. (b). What is the meaning o...