Q1] (A) If F(x+y-z₁x² + y²)=0 where z = z(x, y) дz дz x -y =x-y ax (B) If f(x, t) = f²e-y²dy, then prove that kfxx = ft. and #0 then prove Əz 276 [126]

Q: Find ∂y/∂x1 and ∂y/x2

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Q: The domain of F(x, y) =x*y+ x*+ = 1 D =R²- {(0, -)} A O D=R BO D=R? .C O D=R-{}

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Q: Q1] (A) If F(x+y-2₁x² + y²)=0 where z=2(x, y) and дz дz -у-=х-у ду ах - 0 then prov

A: (.)  Leibniz rule :      Given ,(A).        where   and   .

Q: Let f: R² → R be a differentiable function. (a) At the point (ro. Yo) = (1,5), it is known that the…

A: Given That : Equation of tangent plane to the surface z=fx , y is -2x+3y-z=17. To Find : a)…

Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: Given the function f(x,y)=- 4y? find each of the following. SIMPLIFY A) f,(x,y) =, %3D B) f,(x, y)…

A: Power role of derivative: ddxxn=nxn-1 Derivative of function eax: ddx(eax)=aeax Given function is…

Q: Find the value of fææ + fyy at (1, –1) when 3 + x² + 2y?. xy f(x, y) 1. (frr + fyy)- -7 |(1,–1) 2.…

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Q: Translate Q (0, -8) using (x, y) → (x - 3, y+ 2). Your answer: O Q'(-2, 5) Q' (3, - 10) O Q'(-3, -6)…

A: The transformation is, (x,y) ------> (x-3, y+2) So, (0, -8) ------> (0-3, -8+2)

Q: of have Σ f(m). nez ory" + HAIF bo turn food (A-LAI) - (A) A

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Q: Differentiate: 3 a) F(y) = ( (y + 5y³) x²e* b) f (x) : x2+ex А c) f (x) : B+Cex

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Q: . Find, from first principles, f(2, -1) for f(x, y) = 2a?y³ + e2y. ,2,,3

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Q: Let T: R³ R² be defined by T (E) 2x1 -2x2 + x3 Ex: 5 +2₂] -3 ---(~- -[:] ·~ -E] ·~ -E] --²-(~-…

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Q: Q1. Let f(x, y) = x²y + x + y² +3. (a). Find f(x, y). (b). Find dy

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Q: f(x) = 2/1/2 and g(x)=3x+1, find the following: b) (gof)(x) 8. Let f(x)= a) (fog)(x) c) (fof)(x) d)…

A: according to bartleby guide line we do only first part of multiple questions given  f(x)=1x2  and…

Q: 13. In y = what is the derivative of 2x2 +3? x+1 a) 2x b) 4x c) 4x +3 d) 7

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Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

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Q: W(s, t) = F(u(s, t), v(s, t)), where F, u, and u are differentiable. If u(-6,0) = 6, u,(-6,0) = -2,…

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Q: Which of the following pair of functions is linearly independent? (a) e3*, e(x-3) (b) 4, sin?x +…

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Q: Find V x (V × F) if F(x, y, z) = 9xyj+ 5xyz k. V x (V × F)

A: Given function is F→x,y,z=9xyj^+5xyzk^. To find:  ∇×∇×F→ Concept: Cross product formula for given…

Q: Consider Flx,y) = (3x2 +6y) i t (6x +4y%)j. (as Show that Fis lonservative a function Such Line…

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Q: On which interval(s) is the function g(x) = xª – 8x² + 5 concave down?

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Q: 4y² Given the function f(x,y)= +e*y _find each of the following. SIMPLIFY

A: Given function is, fx,y=4y2x3+ex2y To find fxy(x,y) Find fxx,y partially differentiating the given…

Q: If f(2) = (3z)²a² z+2/a find and simplify f(/@). %3D

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Q: c) Which of the following functions are analytic in 121² 2 2: 42²26649 (ii) Z²-1 Z-√√Z²74

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Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

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Q: Q3/ prove fry = fyx if f(x,y) = x + xy – 5x³ + In(x2 + 1)

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Q: Q/ Let X be the r.v such that E(X) = 2, E(X²)= 2a , E((2+aX)²) = 2a3 Find the value of a. %3D %3D

A: Let X be the random variable such that, E(X)=2, E(X2)=2a, E((2+aX)2)=2a3