Questions from General Calculus

Q: If cos (xyz) = 1 + x2y2 + z2,

If cos (xyz) = 1 + x2y2 + z2, find ∂z/∂x and ∂z/∂x.

Q: Find the directional derivative of f at the given point in the

Find the directional derivative of f at the given point in the indicated direction. f (x, y, z) = x2y + x √(1 + z), (1, 2, 3), in the direction of v = 2i + j - 2k

Q: Find the maximum rate of change of f (x, y

Find the maximum rate of change of f (x, y) = x2y + √("y" ) at the point (2, 1). In which direction does it occur?

Q: Find the direction in which f (x, y, z

Find the direction in which f (x, y, z) = zexy increases most rapidly at the point (0, 1, 2). What is the maximum rate of increase?

Q: Sketch several level curves of the function. f (x

Sketch several level curves of the function. f (x, y) = √(4x^2 + y^2 )

Q: Sketch several level curves of the function. f (x

Sketch several level curves of the function. f (x, y) = ex + y

Q: Each of these extreme value problems has a solution with both a

Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint....

Q: Find and sketch the domain of the function. f (

Find and sketch the domain of the function. f (x, y) = ln (x + y + 1)

Q: Use the Midpoint Rule to estimate the integral in Exercise 1.

Use the Midpoint Rule to estimate the integral in Exercise 1. Exercise 1: A contour map is shown for a function f on the square R = [0, 3] × [0, 3]. Use a Riemann sum with nine terms to...

Q: Calculate the iterated integral. ∫_1^2 ∫_0

Calculate the iterated integral. ∫_1^2 ∫_0^2 (y+2xe^y) dx dy