1. Consider function g(x, y, 2) = z In(a² + y³). (a) Find the gradient vector of g at P(-1,1,2). (b) Find the directional derivative of g(x, y, z) = z In(x² + y³) at P in the direction of i =< 1,1, –1>. (c) Find the direction at which g has the maximum rate of change of g at P. What is the maximum rate?

Q: 4. (a) Determine the directional derivative of f(x, y, z) = zety at the point (1, −1, 1) in the…

A:

Q: (iii) Find the gradient of the function g(x, y, z) = (4√z - x)y² at the point (4, 1, 4) and give the…

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 n = 4 (-x¹ + 22x³ -…

A: (a)How large should n be to guarantee that the Trapezoidal Rule approximation  to is accurate to…

Q: c) Given the scalar function p(x, y, z) = x²e - y³ + cos 2z. Find the directional derivative of p(x,…

A:

Q: Let z = f(x, y) = x² + y² be the temperature at a point (x, y) = R². (a) Draw a sketch indicating…

A: We know that the directional derivative of a function z=fx,y at a,b in a direction v→ is calculated…

Q: (a) Compute the directional derivative of f(x, y) = xy² + x³y at the point (4, -2) in the direction…

A: Since you have posted independent questions, so these are considered as multiple questions.According…

Q: 6. Let f(x, y) = ln(2x - y²). (a) (b) (c) Determine the gradient of f at the point (2, -1).…

A:

Q: 1. Consider the function f(x, y, z) = x²euz² (a) Find the gradient of f at the point (1,3,0). (b) In…

A:

Q: Find the gradient vector and level curve of the following functions at the given point and show that…

A: Given,

Q: 4) Let f(x, y) = x² – 2xy a) Find the gradient of f at the point (1, –2). b) Use the result of (a)…

A:

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: Function: h(x, y) = 9y cos (x - y) (0. E) Point: (a) Find the gradient of the function. -9y sin (x –…

A: we have to solve