Questions from General Calculus

Q: A tank full of water has the shape of a paraboloid of

A tank full of water has the shape of a paraboloid of revolution as shown in the figure; that is, its shape is obtained by rotating a parabola about a vertical axis. (a). If its height is 4 ft and t...

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function.

Q: Evaluate the definite integral. Fe4e dx/x√ ln

Evaluate the definite integral. Fe4e dx/x√ ln x,

Q: The average speed of molecules in an ideal gas is

The average speed of molecules in an ideal gas is Where M is the molecular weight of the gas, R is the gas constant, T is the gas temperature, and is the molecular speed. Show that

Q: The figure shows the sun located at the origin and the earth

The figure shows the sun located at the origin and the earth at the point (1, 0). (The unit here is the distance between the centers of the earth and the sun, called an astronomical unit: 1 AU â...

Q: As we will see in Section 7.4, a radioactive

As we will see in Section 7.4, a radioactive substance decays exponentially: The mass at time t is m (t) = m (0) ekt, where m (0) is the initial mass and is a negative constant. The mean life M of an...

Q: Astronomers use a technique called stellar stereography to determine the density of

Astronomers use a technique called stellar stereography to determine the density of stars in a star cluster from the observed (two-dimensional) density that can be analyzed from a photograph. Suppose...

Q: Determine how large the number a has to be so that

Determine how large the number a has to be so that

Q: Estimate the numerical value of f∞0e-x2 dx by

Estimate the numerical value of f∞0e-x2 dx by writing it as the sum of f40e-x2 dx and f∞4e-x2 dx. Approximate the first integral by using Simpson’s Rule with n = 8 and show that the second integral is...

Q: Show that fπ0x2e-x2 dx = 1/2 f∞

Show that fπ0x2e-x2 dx = 1/2 f∞0e-x2 dx.