Questions from General Calculus

Q: Find the gradient vector field ∆f of f and sketch it

Find the gradient vector field ∆f of f and sketch it. f (x, y) = 1/2 (x2 - y2)

Q: (a). What is the definition of curvature? (

(a). What is the definition of curvature? (b). Write a formula for curvature in terms of r'(t) and T'(t). (c). Write a formula for curvature in terms of r'(t) and r''(t). (d). Write a formula for the...

Q: Determine whether or not F is a conservative vector field. If

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. F (x, y) = (xy + y2) i + (x2 + 2xy) j

Q: How do you find the length of a space curve given by

How do you find the length of a space curve given by a vector function r (t)?

Q: Find curl F and div F if F (x, y

Find curl F and div F if F (x, y, z) = e-x sin y i + e-y sin z j + e-z sin x k

Q: If a lamina occupies a plane region D and has density function

If a lamina occupies a plane region D and has density function ρ (x, y), write expressions for each of the following in terms of double integrals. (a). The mass (b). The moments about the axes (c). Th...

Q: Let f be a joint density function of a pair of continuous

Let f be a joint density function of a pair of continuous random variables X and Y. (a). Write a double integral for the probability that X lies between a and b and Y lies between c and d. (b). What p...

Q: Determine whether or not F is a conservative vector field. If

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. F (x, y) = yex i + (ex + ey) j

Q: Determine whether or not F is a conservative vector field. If

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. F (x, y) = (yex + sin y) i + (ex + x cos y) j

Q: Determine whether or not F is a conservative vector field. If

Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. F (x, y) = (2xy + y-2) i + (x2 - 2xy-3) j, y > 0