Questions from General Calculus

Q: Suppose that Sue runs faster than Kathy throughout a 1500-meter

Suppose that Sue runs faster than Kathy throughout a 1500-meter race. What is the physical meaning of the area between their velocity curves for the first minute of the race?

Q: Determine a region whose area is equal to the given limit.

Determine a region whose area is equal to the given limit. Do not evaluate the limit.

Q: (a). Write the definition of the definite integral of a

(a). Write the definition of the definite integral of a continuous function from a to b. (b). What is the geometric interpretation of fba f (x) dx if f (x) > 0? (c). What is the geometric interpretati...

Q: If r (t) is the rate at which water flows

If r (t) is the rate at which water flows into a reservoir, what does ft2t1r (t) dt represent?

Q: (a). How is the length of a curve defined?

(a). How is the length of a curve defined? (b). Write an expression for the length of a smooth curve with parametric equations x = f (t), y = g (t), a < t < b. (c). How does the expression in part (b)...

Q: An arc PQ of a circle subtends a central angle θ as

An arc PQ of a circle subtends a central angle θ as in the figure. Let A (θ) be the area between the chord PQ and the arc PQ. Let B (θ) be the area between the t...

Q: (a). Explain the meaning of the indefinite integral ff (

(a). Explain the meaning of the indefinite integral ff (x) dx. (b). What is the connection between the definite integral fbaf (x)dx and the indefinite integral ff (x) dx?

Q: Suppose that you push a book across a 6-meter-

Suppose that you push a book across a 6-meter-long table by exerting a force f (x) at each point from x = 0 to x = 6. What does f60f (x) dx represent? If is measured in newtons, what are the units for...

Q: If you have a graphing calculator or computer, why do you

If you have a graphing calculator or computer, why do you need calculus to graph a function?

Q: (a). What is the physical significance of the center of

(a). What is the physical significance of the center of mass of a thin plate? (b). If the plate lies between y = f (x) and y = 0, where a < x < b, write expressions for the coordinates of the center o...