Questions from General Calculus

Q: f (x) = ln x, [1, 3

f (x) = ln x, [1, 3] (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 the...

Q: Of the infinitely many lines that are tangent to the curve y

Of the infinitely many lines that are tangent to the curve y = -sin x and pass through the origin, there is one that has the largest slope. Use Newton’s method to find the slope of that line correct t...

Q: f (x) = 2 sin x – sin 2x,

f (x) = 2 sin x – sin 2x, [0, π] (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 are...

Q: A particle is moved along the -axis by a force that

A particle is moved along the -axis by a force that measures 10/ (1 + x)2 pounds at a point feet from the origin. Find the work done in moving the particle from the origin to a distance of 9 ft.

Q: If 6 J of work is needed to stretch a spring from

If 6 J of work is needed to stretch a spring from 10 cm to 12 cm and another 10 J is needed to stretch it from 12 cm to 14 cm, what is the natural length of the spring?

Q: If f is continuous and f31f(x) dx = 8

If f is continuous and f31f(x) dx = 8, show that f takes on the value 4 at least once on the interval [1, 3].

Q: Find the numbers such that the average value of f (x

Find the numbers such that the average value of f (x) = 2 +6x – 3x2 on the interval [0, b] is equal to 3.

Q: The table gives values of a continuous function. Use Simpson’s Rule

The table gives values of a continuous function. Use Simpson’s Rule to estimate the average value of f on [20, 50].

Q: The velocity graph of an accelerating car is shown.

The velocity graph of an accelerating car is shown. (a). Estimate the average velocity of the car during the first 12 seconds. (b). At what time was the instantaneous velocity equal to the average v...

Q: In a certain city the temperature (in 0F) t hours

In a certain city the temperature (in 0F) t hours after 9 AM was modeled by the function Find the average temperature during the period from 9 AM to 9 PM.