Questions from General Calculus

Q: Use Equation 6 to find dy/dx. Equation

Use Equation 6 to find dy/dx. Equation 6: ey sin x = x + xy

Q: Find the local maximum and minimum values and saddle point(s

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the impor...

Q: The temperature T in a metal ball is inversely proportional to the

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball, which we take to be the origin. The temperature at the point (1, 2, 2) is 1200. (a). Find the r...

Q: The temperature at a point (x, y, z)

The temperature at a point (x, y, z) is given by where T is measured in 0C and x, y, z in meters. (a). Find the rate of change of temperature at the point P (2, -1, 2) in the direction toward the po...

Q: Suppose that over a certain region of space the electrical potential V

Suppose that over a certain region of space the electrical potential V is given by V (x, y, z) − 5x2 - 3xy + xyz. (a) Find the rate of change of the potential at P (3, 4, 5) in the direction of the ve...

Q: Show that the operation of taking the gradient of a function has

Show that the operation of taking the gradient of a function has the given property. Assume that u and v are differentiable functions of x and y and that a, b are constants. (a). ∆ (...

Q: The radius of a right circular cone is increasing at a rate

The radius of a right circular cone is increasing at a rate of 1.8 in/s while its height is decreasing at a rate of 2.5 in/s. At what rate is the volume of the cone changing when the radius is 120 in....

Q: The second directional derivative of f (x, y) is

The second directional derivative of f (x, y) is

Q: Let R(s, t) = G(u((,

Let R(s, t) = G(u((, t), v(s, t)), where G, u, and v are differentiable, u(1, 2) = 5, us(1, 2) = 4, ut(1, 2) = -3, v(1, 2) = 7, vs(1, 2) = 2, vt(1, 2) = 6, Gu(5, 7) = 9, Gv (5, 7) = -2. Find Rs (1, 2)...

Q: The pressure of 1 mole of an ideal gas is increasing at

The pressure of 1 mole of an ideal gas is increasing at a rate of 0.05 kPa/s and the temperature is increasing at a rate of 0.15 K/s. Use the equation PV = 8.31T in Example 2 to find the rate of chang...