3: Assume that g(s) is an increasing function and define f(x, y) = g(x² + y²). Show that the angle between Vf(a, b) and u = (a, b) is 0.

Q: Let = (3, 4, 12) . Find the directional derivative of f(z, y, 2) =1– y² +32³ in the direction of v.

A: Consider the given function, fx,y,z=x-y2+3z3 and v=3,4,12 Now, find the derivative of the function…

Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

Q: Consider a function f: R? → R°, the derivative of f isa O 3 x 3 matrix O 3 x 2 matrix O 2 x 3 matrix…

A:

Q: Consider the function f : R2 → R given by f(x, y) = xy³ + ye*-2. (a) For each of the following…

A:

Q: Evaluate Əw at (u,v) = (1,2) for the function w(x,y)=xy-y²; x = u-v, y = uv. ди OA. -1 B. 3 O C. 1…

A:

Q: Decompose the function y=(4-2x3)4 in the form y=f(u) and u=g(x)   use g(x) = 4-2x3

A: Given function      y=4-2x34  then  we have  to decompose  the given  function  in the form  y=fu…

Q: Consider the (x, y) table below: X y 1 48 2 72 3 108 4 162 Find a function of the form f (x) = a b…

A:

Q: Sketch a contour map of the function. f(x, y) = x² + 7y² y

A: The given function is .To determine the contour map and the sketch of the function.

Q: Let u and v be the linear functions defined asu(x)=2x+3,v(u)=3x-2.Find the compositions u*v and v*u.…

A: For uov, we do u(v(x)), and for v o u, we do v(u(x)) .

Q: Let f: R2 R2 be the function given by f(x, y) = (x + y, y). Prove or →>> 8. disprove: f is…

A: Function which is one to one

Q: he function f(x)=3x2+2x

A: Introduction: A function is bijective if it is both injective and surjective and a function f(x) is…

Q: Find the gradient function for: 21y-

A: