x+y if (x, y) # (0,0) (1 if (x,y) (0,0) Q.3 ( 3+3+4) (a) Prove that the function f(x, y) is not continuous 2x+y %3D at (0,0).

Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: Find all first partial derivatives. f(x, y) = 9x° + 4y – 5 9x3 + 4y – 5 f,(x, y) f,(x, v) =

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Q: f(x, y) = 3x² - y x4 x² + 2y ² 1 (x, y) = (0,0) 2 D (X,Y)= (0,0) 1 Determine if f is continuous at…

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Q: Both first partial derivatives of the function f(x.y) are zero at the given points. Use the…

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Q: 1 If f(x, y,z)= ôf then 2у - х —z a. 2 (2y-x-2) b. 1 (2y -x-2)2 с. -1 (2y –x-2) d. 1 (2y–x-2)

A: It is derivative problem.

Q: (Wronskian) of the functions y1, Y2, Y3 defined below with constants a, b, c). Y1 (x) = 7a + 5x;…

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Q: du -xy du Ifu =f(x² +2yz,y² +2zx) Prove that (y- zx)-(x² - yz) -NX ду

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Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

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Q: 4. Finding partial derivatives w.r.t "x" F(x,y,z) = xy°z* + 3yz?

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Q: xy(x² – y²) if (x, y) # (0,0) Let f(x, y) x2 + y? Show that fi(0, y) = -y for if (x, y) = (0,0) all…

A: Here, the given function is: f(x,y)=xy(x2-y2)x2+y2, if x,y≠(0,0)0                  , if (x,y)=(0,0)…

Q: 2. The second order partial derivatives Fxx(x,y) of the function ( F(x,y) =x'y- In (x'-y)) equal .

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Q: (x* + y° ) In (x² + y* ). (x,y)= (0,0) f(x, y) = k +1, (x, y) = (0,0)

A: If f is continuous then lim (x, y) tends to (0, 0) =k+1 And using l hospital rule.

Q: The function f(x, y) = xª + yª – 4.xy has three critical points, (0,0), (1, 1) and (–1, –1). At the…

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Q: Using TSE: dy 3D f(x, у) %3 3х — 2у dx f = 3x – 2y f' = ar +af = 3+ (-2)(3x – 2y) = 3 – 6x + 4y of…

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Q: Suppose that the Second Derivatives Test is applied to a real-valued function z = f(x, y), whose…

A: Given real value function is z=f(x, y) and second derivatives are continuous on the disk D centered…

Q: * (0,0) is not continuous if (x, y) Q.3 ( 3+3+4) (a) Prove that the function f(x,y) = {2x+y (i if…

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Q: f(x) has local minima at x = i and x = i f(x) has a global maximum at x = i f(x) has a global…

A: The critical points of any function are the points where the derivative of any function vanishes or…

Q: 13 Find the linearizatian z=L(x.y) f the function 2=f(x.y) =4x²-y²42y at the point (x.y) = (3,2).…

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Q: ( x+y if (x,y) # (0,0) Q.3 ( 3+3+4) (a) Prove that the function f(x,y) = 2x+y is not continuous (1…

A: We apply two path test for proving the discontinuity of function

Q: 7. f(x) = x² In x, f"'(x) 1 8. y = -, y" 1 .f"(q) 9. f(q) = 2g* 10. f(x) = /x, f"(x) 11. f(r) = /9 –…

A: The objective of the question is determine the derivative of the given function "y".

Q: if the function u= ln (x^3+x^2y-y^3/x-y) then x su/sx + y su/sy is

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Q: 2² – 6y? Then Let f(x, y, z) y2 + 4z² fz(x,y, z)= fy(x, y, z)= f-(x, Y, z)=

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Q: Both first partial derivatives of the function f(x,y) aro zero at the given points. Use the…

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Q: 114 f(x, y) = (xy²-1 y-1 tion f(x, y) at the point (1,1), where (x, y) = (1,1) (x, y) = (1,1)

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Q: 1 (x, y) = (1, –1) f(x, y) = x2 + Y (æ, y) + (1, –1) x + y is not continuous at (1, –1). [b]

A: Given :    f(x, y) = 1 ,(x, y) = (1, -1)x2+yx+y ,(x, y) ≠ (1, -1) To show :   f is not continuous at…

Q: t2 +1 1 2t2 – t – 1 - (ш) f(t) = 1+ - 2t2 – t – 1'V t' x² + 1 - Væ + y +1 (IV) f (x, y) ,x In (y² –…

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Q: bounded.y- Find the areet of the reyion h- and. the line-Y.DX+2 2. 2. O I= y-y and the line y=-x-…

A: We have to find the area of the region R bounded by a. x=-y2 and the line y=x+2b. x=y-y2 and the…

Q: dy + 2xy = f(x), y(0) = 6, where dx f(x) = lo, x, 0sx< 1 x 2 1 0 sx < 1 y = x 2 1 Use a graphing…

A: Linear differential equation of first order : The most general form of a linear differential…

Q: dy Find a continuous function function y on (-0,00) satisfying -6/7 = 9x dx and y(-1)= -4. dy -6/7…

A: Given query is to solve the differential equation.

Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: From the given information the given curves from which the volume is to be generated are:

Q: f(x) is a twice differentiable function with f(0) = 4, ƒ(1) = 3, f'(1) = 6, Then So 3xf" (x)dx =

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Q: 4. x* · y f(x, y) (x, y) # (0,0); x4 + y2 f (0,0) = 0, (x, y) = (0,0). Calculate a formula for the…

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Q: ∇⋅F of F = (2x3y)i-(3y2z)j+(xz3)k at (1,2,-1). a. 27 b. -34 c. 4 d. -7

A: The del operator is used to represent the partial derivatives with respect to the variables defined…

Q: Both first partial derivatives of the function f(x,y) are zero at the given points. Use the…

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Q: e-(z-1)2-y 1 (r, y) # (1,0) If f(r, y) = (I-1)2+y (r, y) = (1,0) %3D is continuous at (1,0), what is…

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Q: 2x lerivatives from first principle, find the derivatives of y = 5 V3x-e2x-(xln x)(In(In x)) -2e2x)…

A: We have to find the derivative from the given function

Q: V4–x² – y² Let f(x,y) =- Shade the region in the x-y plane that corresponds to the domain of f(x,y)…

A: We are given the function f(x, y)=4-x2-y2lnx-y. For f(x, y) to be defined, we must have the domain…

Q: Minimize f(x1,x2,*3) = (x1 – x2) + (x2 - x3)* subject to 8,(X) = x,(1 + x) + x - 3 = 0 -3 < x; s 3,…

A: Given: Minimize fx1,x2,x3=x1-x22+x2-x34 subject to g1x=x11+x22+x34-3=0 -3≤xi≤3,i=1,2,3.

Q: f: (Z, +) → (Z, +) where f(x) = 2x. f: (R, +) → (R*, .) where f(x) = 2*

A: We will use definition of isomorphism

Q: 1. f(x, y) = 1- x - y 2. f(x, y) = xy 3. f(x, y) = Vx² + y² 2

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Q: (x+ 1)ª – y² (x + 1)4 + y² - if (x, y) # (–1,0) et f(x, y) -1 if (x, y) = (-1, 0) Show that f is not…

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Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: (x2 + y2 + z²)5 = -23. Calculate əz/ax using implicit differentiation. O əzləx = x/z O əzləx = 2x/z…

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Q: F(x) = (2t – 1)³ dt - using the Fundamental Theorem of Calculus. 25 F'(x) =…

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Q: 2xy F(x, Y) =Vx+ 2y (1, 1) f,(x, y) = 1,(1, 1) S(1, 1)

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Q: dz -2zFw * + 2г Fw

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Q: find absolute maximum and minimum of f(x,y)=x^3+3xy-3y^2+2 in a region whose vertices at (-1,-1)…

A: Given function is  fx,y=x3+3xy-3y2+2

Q: ntegrais. I, da, D= {(x.y) 0sxs20sys2% dA, D = x +2 [['e"d4, D={(x,y)| 0s ys 4,0sx<y}

A: Double integration