{ z sin a). if (x, y) # (0,0) 2. Determine if a function f: R2 R defined by (. 9) = BE 0, if (KJ) = (0,0) %3D is continuous at (0,0).

Q: S (x, y)= I+x* + y? 1-x² - y? 2. Determine the points at which the function is continuous.

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Q: Isin , it (z, y) # (0, 0) 2. Determine if a function f : R → R defined by f (r, y) = 0, if (z, y) =…

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Q: Show that the function f(z)= Im(z) is nowhere differentiable.

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Q: The function z is defined by z(x, y) = x y-3 y Find A z and dz when x= 3, y= 5, Ax = - 0.04 and A y…

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Q: Q2] Find the analytic function F(z) if u = coshy.cosx, (B.C. v-0 at x=0)

A: at

Q: The x and y coordinates of the inflection point(s) of the function f(x) = x + 21x* is (are): A. No…

A: Solution :-   Given fx = x3+21x2We have to find inflection point for this, we put f''x = 0

Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

Q: Evaluate F.dr where F(x, v)=xyi (4, 0).

A:

Q: Assume that y is a function of x. Find (d2y)/(dx2) for x2y-y2-2(sqrt x)+4=0 at point (1,2) 7/6 8/6…

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Q: Find and sketch the domain of the function f(x,y) = cosx + V3x-y+2

A: The given function is .The objective is to find the domain of the function and sketch the domain.

Q: 49y" — 42y + 5y = 0, and - y(4) = 4, y'(4) = 1. y =

A: 49y''-42y'+5y=0, y(4)=4, y'(4)=1 Auxiliary equation 49m2-42m+5=0

Q: if r'y-- 2y + 1.

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Q: Determine if the following functions are analytic or not: 1. f(z) = (z* + 1)³ – 3z* where z is the…

A: (i) The  given function is ;               fz = z*+13 - 3z* We know that a function  f is analytic…

Q: the doi n ain of the functions

A: We have given two functions : f(x,y)=1xy…

Q: I. Determine whether or not the function x2 + 2y if (x, y) # (0,0) f(x, y) 1 er-y if (x, y) = (0,0)…

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Q: 4 Let f(x) = 6x°va + || f'(x) =

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Q: 3. Find all functions from X = {a,b} to Y = {p,r, t}.

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Q: Let F(x, y) = . Evaluate (3,2) SF.. (1,-1) F.dr

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Q: Find y as a function of a if y(1)=2, y(1) = 1. y = r²y" + 7xy +9y = 25,

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Q: Find the analytic function f(z) = u + iv if u = 2 cos x .cosh 2y cos 2x + cosh 2y

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Q: Let F = (4xyz + 7 sinx, 2x², 2x²y). Find a function f so that F = Vf, and f(0,0,0) = 0.

A: To find the function f such that F=∇f, we need to find the potential function whose gradient is…

Q: 5x6y² if (x, y) = (0,0) Determine if f(x, y) = {(x² + y²) ² +y²)² if (x, y) = if (x, y) = (0,0) 0…

A: