f(1, 1) = f₁(1)f₂(1) f(1, 2) # f₁(1)f₂ (2) for x = 1, y = 1,2 then x and y are: dependent O independent O

Q: x?y x² + y² Define the function f: R² → R by ƒ(x, y) = if (x, y) # (0,0) if (x, y) = (0,0) (a) Let e…

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Q: Em f(x) is equivalent to g(0) when f= x O True and g(x)=x O False

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Q: The antiderivative of the function f(#) + 8* is -8 + 2.0a2 +e 4 +4.0a2 +c -4 + 16.0a? + c -4 4.0a2 +…

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Q: Q10

A: Given F(u,v)be a function of two variables. let Fu(u,v)=G(u,v) and Fv(u,v)=H(u,v) Here f(x)=F(u,v)…

Q: Use the table to determine Df(g(x)) at x = 3. |1 2 f(x) 1 3 4 3 2 f(x) 3 -5 1 4 g(x) 2 4. 4 1 3…

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Q: A. Show that f(x, y) = (x-1)(y-2) (x-1)²+(y-2)² 7 (x, y) = (1,2) (x, y) = (1,2) at (1,2). 1 is…

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Q: 20 20 Let f be a continuous function such that | f(x) dx = 8, [ f(x) dx = – 3, and f" f(x) dx = 7.…

A: According to the interval addition of integrals, a definite integral can be split into two integrals…

Q: 3. Given fxx(x,y)= 4x² On Support 0 Otherwise Let U=Y-X. Determine f(u) (Including the Support of U)…

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Q: different directions and the (x-1) If 4 7 (x-)? If y =(x-1)2 • Determine f is contincous in (1,0)…

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Q: The value of c of fox) -x*-2 x", in the interval [-2,2) such that f'(c) -0 is .A -1 ,2 ,0 .B -1,1 .C…

A: We apply mean value theorem Answer c)-1,0,1

Q: f(x,y) = –x² + 2xy + 3y² – 6x – 2y – 4 | - Serialize the function around the point (-2,1). a) f(x,y)…

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Q: Suppose f: X→ Y, and A, B CY. Prove that (a) f¹(AUB) = f¹(A) U f¹(B).

A: Union of two sets A and B is denoted as A∪B  It contains all the elements that are either in A or in…

Q: (3) Determine the values of a for which x4 + y* , if(x, y) # (0, 0), (x² + y?)ª f(x, y) = ,if(x, y)…

A: solution.

Q: (Q1)-A-State(First fundamental theorem) and Show that :(2₂0 /(10), +..) -B-Let f:( M, (Z).+-)-(M,…

A: As per the policy, we are solving first question. Please repost it and specify which question is to…

Q: F . dr, (c) Let f(x, y, z) = x³ + 2yª + 325 and F consists of three line segments from (1,0, 0) to…

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Q: (b) The function f depends on u, v and t so that f(u,v,t)=u²+v+2t It is further given that (i)…

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Q: 1. Let f(x, y): x-y x+y+1 Find:

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Q: dy Let y = x?Vx2 + 1 then is dx x (3x2 + 2) Vx2 + 1 x² +1 A (3x2 + 2) Væ2 +1 B x² + 1 2x2 (3x2 + 2)…

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Q: Find the values of af /ax and af lay at the point (4, 5) if f(x,y)=x² + 3xy + y -1

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Q: Let f(x, y) = x³ + y3 – 9xy + 27, then (3,3) is saddle point. True False

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Q: (ii) Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1,2) = 3, gs (1, 2) = −1, gt(1, 2) = 4,…

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Q: The domain of the function f(x, y) = - In(x² + y²-1) is:

A: The function fxgx is defined for gx≠0 The function lnx is defined for x>0

Q: ху af If f(x,y) then is %3D x2+y ax

A: Given function,  fx,y=xyx2+y

Q: z} 0,1} definition for f: X→ A that is a well-de- (0, w), (-1, w), (-2, w)} , (0, w), (-1, w), (-1,…

A: We have to choose the correct option from the given options according to the given information

Q: f(x, y, z) = ay +æ? – y? function faz + fyy + f zz = 0 It is a function that provides equality- True…

A: Given,f(x,y,z)=xy+x2-y2Now,differentiating both the sides w.r.t x,y and z…