Questions from General Calculus

Q: Find the exact area of the surface obtained by rotating the given

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Q: Find the exact area of the surface obtained by rotating the given

Find the exact area of the surface obtained by rotating the given curve about the x-axis.

Q: Find the surface area generated by rotating the given curve about the

Find the surface area generated by rotating the given curve about the y-axis.

Q: Find the surface area generated by rotating the given curve about the

Find the surface area generated by rotating the given curve about the y-axis.

Q: Find the radius of convergence and interval of convergence of the series

Find the radius of convergence and interval of convergence of the series.

Q: Use Formula 1 to derive Formula 6 from Formula 8.2

Use Formula 1 to derive Formula 6 from Formula 8.2.5 for the case in which the curve can be represented in the form /

Q: (a) Show that the curvature at each point of a

(a) Show that the curvature at each point of a straight line is / = 0. (b) Show that the curvature at each point of a circle of radius r is / = 1/r.

Q: A cow is tied to a silo with radius r by a

A cow is tied to a silo with radius r by a rope just long enough to reach the opposite side of the silo. Find the grazing area available for the cow.

Q: Sketch the curve by using the parametric equations to plot points.

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.

Q: Sketch the curve by using the parametric equations to plot points.

Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases.