Approximate fx(1,3) using the contour diagram of f(x,y) shown below.

Q: Find fy (x, y) for f(x,y) ry

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Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

Q: Calculate the gradient. f (x, y) = cos(x^2 + y)

A: Calculate the gradient. f (x, y) = cos(x^2 + y).

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx at the point (1,-1,1) in the direction…

A: Directional derivative using gradient

Q: The function f(x, y, z) = x² − y² − z ² increases in the direction 〈六〉 (1, 1, 1). at the point

A: Please check step 2 for solution.

Q: Express in form y=f(x) by eleminating the parameter x = t + 3, y = 4t

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Q: Use the gradient to find the directional derivative of the function at P in the direction of Q. f(x,…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

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Q: Calculate fxxyz for f (x, y, z) = y sin(x + z).

A: We first differentiate the given function with respect to x twice. Then y and z will be treated as…

Q: Evaluate f z²dz where C is the contour |z| = 2-

A: We can directly use cauchy Goursat theorem to give the value of the given integral about given…

Q: Evaluate F dr, where C goes along the curve {x* + y* = 1, z = 2} from (1,0, 2) to (b) (0, 1, 2).

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Q: Calculate fxxyz for f(x, y, z) = y sin(x + z).

A: For a function in several variables, partial derivative with respect to one variable say x can be…

Q: Find the directional derivative of the function at P in the direction of v. F(x, y) = x³ - y, P(8,…

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Q: Sketch a contour diagram for f(x, y) = x2 − 2y2 with three labeledcontours.

A: To sketch the contour diagrams for the given function of two variables

Q: find fy CX,Y) it (x,Y)=x2-8xy- 2y?

A:

Q: Find the linearization of the function f(x, y) 155 – 2x2 – 5y² at the point (5, 4). L(x, y) = Use…

A: Given:      f(x,y) = √ (155 - 2x2 - 5y2 )     Point : ( 5 , 4 )  Now     Linear approximation f (…

Q: y = Vx+V

A:

Q: How will the contour maps of f (x, y) = x and g(x, y) = 2x with contour interval 1 look different?

A: To describe how the contour maps of f(x, y) = x and g(x, y) = 2x with contour interval 1 look…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: Which direction is the directional derivative of the function f (x,y, z) = x2 – 2yz at point…

A: Solution: The function is fx,y,z=x2-2yz The point is P1,1,1 We have to find the direction in which…

Q: Find the direction derivative of f(x.y,z)-xy'z at the point p(3.2,1)in the direction towards…

A: given function, f(x,y,z) = xy2z3 first we need to find the gradient(∇f) of this function at point…

Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: Find gyy when g(x,y)= (x/y)

A: Given function is Differentiating partially with respect to y, we get

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Use the gradient to find the directional derivative of the function at P in the direction of  PQ.…

A: This is question of application of differentiation which we will proceed as follows

Q: y = VT, y = 2 - x and r O about the x-axis?

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Q: • Find the direction in which f(x,y) = yeY increases most rapidly at the point (0, 2). %3D

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Q: Find and determine type of stationary point for ƒ(x,y)=x' – 3x² + 2xy – y

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Q: Find fyry. f (x, y) - = x"y" – 9x°y + x f yry %3D

A: Partial derivatives are calculated with respect to y then x and again with respect to y.

Q: Sketch the contour plot of f(x, y) = 4x² + y² using level curves of height k = 0, 1, 2, 3, 4, 5.

A: Given: f(x,y)=4x2+y2 Let 4x2+y2=k. Now graph contour plot for k=0,1,2,3,4,5.

Q: Find fg, fyand f; if f(x,y,z) = x - Vy² + z²

A: Given:     To determine: Partial  derivative  fx, fy, fz

Q: f(x,y)=x^2+9y^2 What is the direction in which f changes most rapidly at point (1,2)?

A:

Q: Find the direction derivative of f(x,y)= Xe ² + y ² at the paint (2,1), by the dirction of V = i- j

A: Topic:- application of derivatives

Q: Consider the function f (2)= +-z Which direction is a descent direction at z (1,1)?

A: This is a problem of vector calculus.

Q: Find the linear approximation to f (x, y, z) = 3, -3, – 1): at the point | F(x, y, z) ×

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Q: Find fyry. f(x, y) = a°y® – 6æ*y+x fyry =|

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Q: Calculate the gradient. 5x g(x, y) = x² + y? (Use symbolic notation and fractions where needed. Give…

A: first calculate the gradient for partial differentiation.

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: Find fy (X,y) if f(x,y) = (x° + y°)°. ху Exy(x.y) =

A: Topic: differentiation

Q: Evaluate 2-1 dz where C is contour defined by lz-3il: 113

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Q: · y = Vx - x, (1, 0)

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Q: Find the tangent plane to the equation z = x2 + 5y² + 3y at the point (-5,-2,39)

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Q: Find when z% = xy, where x = f(t) and y = g(t) %3D

A: Given that z=xy2, x=ft and y=gt find ∂z∂t

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 0.…

A:

Q: Find the directional derivative of f at the given point in the direction indicated by the angle θ.…

A: To determine the directional derivative of function f(x, y)=2ye-x at point (0, 1) and direction is…

Q: Approximate V(7.992) + (80.998)i using tangent plane

A: In this question we need to find the equation of the tangent plane and by using the appropriate…

Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

A: