22. lim (x, y)→(0,0) 1 - cos (xy) xy

Q: 4. lim xy (xy)-(0.0) v2-e-1

A: To evaluate limx,y→0,0xy2-exy-1 Substitute t=xy, then as x,y tends to 0,0 implies t tends to 0.…

Q: Sin (πω) lim W→-4 w? sir ω 6!

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Q: Consider the function f defined by 1²+y² V12+y?+1-1 ,2 f(r, y) = %3D lim(7.y)¬(0,0) f(x, y) =

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Q: If f (x, y) = xcos (xy) then find fæ. cos (xy) – ysin (xy) O cos (y) – xysin (xy) O cos (xy) + xysin…

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Q: lim (x.y)-(0,0) cos( x² +y2 (x, y) # (0,0) f(x, y) = (x, y) = (0,0) %3D is continuous at (0, 0).

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Q: x2 – 1- y lim (x,y)→(1,0) X – Vy +1

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Q: 3. Let h(x, y) x + y sin²x 2¹+ y² 0, if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: 8. Let g(r, 9) = (a) Show that g is harmonic in D- {(7,9) : + (y +3)2 < 4}. (b) How can the funetion…

A: Here given as gx, y=yx2+y2 ......(1)

Q: Consider the R 2 − R function f defined by f (x, y) = x − 2y. Prove from first principles that lim…

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Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: fyx if f(x, y) = sin(xy) + x² In y

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Q: Let f(x, y) lim (x,y) →(0,0) (x,y) ES₁ O 3 2 3xy x² + y². f(x, y) = 0 3 O 6 5 = If S₁ is the set of…

A: Let f(x,y)=3xyx2+y2 If S1 is the set of points along the line y=2x Then we have to find the…

Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: y — у — 2 3. lim f(y), where f (y) = y→2 y2+ у — 6

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Q: Let f(x, y) = + tan(xy – x³) , find дудх x-4y5 O a. 80y4 + sec2(xy – x³)(1+ (xy – 3x³) tan(xy – x³))…

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Q: 2y-n у-п lim п cos y y-

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Q: Let h(x, y) = x5 + y sin²x x² + y² 0, { 25 if (x, y) = (0,0) if (x, y) = (0,0) (a) Show that h is…

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Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Find lim Δx-0 f(x + Δx) = f(x, y) ΔΧ for f(x, y) = −2x – 9xy + 2y.

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Q: lim (1,4)→(0,0) r2 + y8

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Q: 5. Let f(x, y) = sin(2.xy). Find f.(x,y) A) f,(x,y)= 2xcos(xy) B) f,(x,y) = 2y cos(xy) C) f.(x,y)= 2…

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Q: + y sin²x -4 + y² 0, if (x, y) = (0,0) if (x, y) = (0,0) = discontinuous at (0,0). 0).

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Q: 5xy sin ³²x + 3y² 0, f(x, y) (a) Prove that lim T if (x,y) + (0,0) if (x,y) = (0,0) f(x,y) does not…

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Q: 9) If y = sin(sinæ), then y' is: x + 2| lim (x +3) I→-2- x + 2

A: See the attachment

Q: (b) lim Y-0 1- cos y Y = 0

A: Our Aim is to evaluate the limit of the expression given below and proof it equal to…