Questions from General Calculus

Q: Show how to approximate the required work by a Riemann sum.

Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A heavy rope, 50 ft long, weighs 0.5 lb/ft and hangs over the edge of a building 120 f...

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

Suppose f is continuous on [0, ∞] and limx→∞f (x) = 1. Is it possible that f∞0f (x) dx is convergent?

Q: A CAT scan produces equally spaced cross-sectional views of a

A CAT scan produces equally spaced cross-sectional views of a human organ that provide information about the organ otherwise obtained only by surgery. Suppose that a CAT scan of a human liver shows cr...

Q: A log 10 m long is cut at 1-meter intervals

A log 10 m long is cut at 1-meter intervals and its cross-sectional areas A (at a distance from the end of the log) are listed in the table. Use the Midpoint Rule with n = 5 to estimate the volume of...

Q: (a). If the region shown in the figure is rotated

(a). If the region shown in the figure is rotated about the x-axis to form a solid, use Simpson’s Rule with n = 8 to estimate the volume of the solid. (b). Estimate the volume if t...

Q: Find the volume of the solid obtained by rotating the region bounded

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

Q: (a). A model for the shape of a bird’s egg

(a). A model for the shape of a bird’s egg is obtained by rotating about the -axis the region under the graph of Use a CAS to find the volume of such an egg. (b). For a Red-throate...

Q: Find the volume of the described solid S. A right

Find the volume of the described solid S. A right circular cone with height h and base radius r.

Q: Find the volume of the described solid S. A frustum

Find the volume of the described solid S. A frustum of a right circular cone with height h, lower base radius R, and top radius r.

Q: Investigate the family of functions f (x) = ln (

Investigate the family of functions f (x) = ln (sinx + C). What features do the members of this family have in common? How do they differ? For which values of C is f continuous on (-∞, ∞)? For which v...