z sin (), if (2, y) # (0, 0) 2. Determine if a function f : R2 → R defined by f (x, y) = %3D 0, if (r, y) = (0,0) %3D is continuous at (0,0).

Q: f(x, y, z) = xy°z +x*yz² – sin xy + cos yz Which of the following is the 1st order derivative of the…

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Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Find the derivative of the function h (x, y, z) = cos xy+ e+ In zx %3D at P. (1, 0, 1/2), in the…

A: Here we have to find directional derivative of h(x,y,z) in the direction of u.

Q: dz Use the Chain Rule to find dt for z = x2 + y2 + xy,x = sin t , y = e'.

A: z=x2+y2+xy ; x=sint , y=et

Q: 4x Find the linearization L(x,y) of the function f(x,y) = e cos (5y) at the points (0,0) and 0,

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Q: f(x.y) =e^sin(y) + In(xy) ; әз of Әхд-у

A: Given: fx,y=exsiny+lnxy To find the partial derivative of ∂3f∂x∂2y Partial differentiation: Partial…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: Find the linearization of the function f (x) = x at a = 1. a Va lal sin (a) L (1) Using this…

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Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: { z sin a). if (x, y) # (0,0) 2. Determine if a function f: R2 R defined by (. 9) = BE 0, if (KJ) =…

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Q: B: Expressand as functions of u and v both by using the Chain Rule and by expressing z directly in…

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Q: Consider the function z=x ln(1+ y“), if x=2-t and y=\t , use an appropriate form dz of the chain…

A: According to the given information, consider the given function z.

Q: If f(x) = xe , x >0 and (Y = ln(X)), then the PDF of Y is %3D (In(1)² (In(y))e ye

A: Answer: ⊙ ey-12e2y

Q: 1. Consider the function f(x, y, z) = x² + 2y + 2², which is differentiable at (2,1,1). 1) find…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: 3. Find the total differential of z = f(x, y) if z2 - y = (1– 2x)z.

A: Total differential of a function z=fx,y is dz=∂z∂xdx+∂z∂ydy

Q: A function (f) is homogeneous of degree • if and only if : ôf + y = Af (x, y). Does the function…

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Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: Let w(x, y, z) = x² + y² + z² where x = sin(7t), y = cos(-3t), z = e-4t. dx dy dz dw dt dt' dt dt…

A: Given problem:- wx,y,z=x2+y2+z2,x=sin7t,y=cos-3t,z=e-4t Find dwdt

Q: 10. Find the linearization, L(x,y,z) of the function f (x, y, z) = e* + cos(y + z) at Po (0,",").

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Q: Find the linearization of the function f (x) = x at x = 1. a lal sin (a) L (x) Using this…

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Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: Consider the following function: f(x,y) = { (x2+y2)sin[1/(x2+y2)], for (x2+y2) not equal to 0; 0,…

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Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: {[{ ال 1: تحق ق من دالة التالية تحق ق معادلة لابلاس :س Z = In /x2 + y² اضف ملف ك 3. fxy ل لدالة :…

A: To find  Partial derivatives of the given functions

Q: Use the appropriate multivariable chain rule to find the indicated derivative. a. Let w = f(x,y,z) =…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: If x, y, and z are lengths of the edges of a rectangular box, the common length of the box’s…

A: Given If x, y, and z are lengths of the edges of a rectangular box

Q: Let y= tanx .(a) Find the differential dy .(b) Evaluate  dy and ∆y if x= and π /4 and dx =-0.1.

A: Given function is (a) Differentiating with respect to x, we get

Q: Find the linearization of the function f (x) = x° 26 at æ = 1. a vā |a| sin (a) L (x) = Using this…

A: I am going to solve the given problem by using some calculus to get the required result.

Q: (4) Let f(x, y) = e-y. Find the linearization of f at an appropriate point and use it to…

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Q: 1. (a) Let f(r,y)- cos(z + 2y). Compute the diectional derivative Df(r,9), where u- (b) Compute ff,…

A: Solve the following

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

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Q: Find the linearization of the function f (x)= x³ at x = 1. qb |a| sin (a) L (x) = Using this…

A: Given, fx=x5 We know that, If we have a differentiable function f defined near "a" the linearization…

Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: 2. Suppose that z = f (x, y) and both x and y are functions of a single variable t such that dy t2 –…

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Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: If = Z sin x = 2t, y = 2 – t2, find dz/dt using the chain rule. Assume the variables are restricted…

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Q: Assume x and y are functions of t. Evaluate dy for 4xy - 7x+4y3 = - 48, with the conditions dt dx =…

A: Explained below

Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: Let w(t) = ((g(t))^2 + 1))^1/3, where g(t) is a continuous function. If g(t) = √7 and g'(0) = 2,…

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Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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Q: implicitly dx

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Q: Find the linearization of the function f (x) = =° at z = 1. L (1) = Using this linearlization, ƒ…

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Q: Suppose f(x) = x2 + sin x and F is an antiderivative of f that satisfies F(T) = 0. %3D Then F(x) =

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Q: Find of /dy if f(x, y) = y sin(xy) 1 + xycos(xy)csc(xy) csc(xy) B) xy cos(xy) + sin(x) A) O

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