Let f(x, y) = √x+9-√√y+9 x-y m if x #y if x=y then f(x,y) is continuous at (0,0) if:

Q: 1+х f[X_, Y_] := 2 у - 1-x (1+) (у-1)2

A: We will use basic knowledge of the functions of several variable theory to answer this question.  We…

Q: 2x - 3x + 13x+a if x#2 f(x) = . X-2 b if x = 2

A: Solution:- It is give that f(x) is continuous at x=2  and the given function is  f(x)=…

Q: Find the domain and range of:

A: (a) We know that the domain of the square root function is always greater than equal to 0. Thus,…

Q: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that f…

A: Let f:R-->R and suppose that |f(x)-f(y)| less than or equal to |x-y|^a for some a>1. Show that…

Q: Is there a real function f(x) that is differentiable only at a point x?

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Q: Is this function analytic fizz=. (1 +x)? +y2 2

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Q: Q3) If f(z) is analytic function and u(x, y) = x3 – 3xy find f(z)

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Q: Q3-A) Is the function F(Z) continuous or not at z-U? 1+|21,

A: Let z = x+iy then Re(z) = x and |z| = √(x^2 + y^2) If z = 0 => x = 0 and y = 0

Q: Q2/Show that the functions is harmonic u = 2 x (1 - y)

A:

Q: Let f(x, y, z) = x³ + 5x²yz + 3xz+ 3, v = Then: D, f(a) = 201 0 -2 and a = -5 2 -5

A: Given that f(x, y, z) =x3 +5x2 y z +3xz+3 The directional derivative is a concept from multivariable…

Q: Are these functions injective or surjective?  f : R → R; f(x) = x^2,  f : R → Z; f(x) = bxc,  f :…

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Q: find the first derivative f'(x) at the point x 1.3. Use two point central difference

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Q: find the critics (local max, lo cal min) Of the function f(xcy)= -x5+ Dy3+27x-24y+3

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Q: Let f(x, y) = √√/175 – 3x² – 4y² Evaluate f(1,4)

A: Given :To Find :

Q: Use Green's Theorem to evaluate F = (xy + y²)i+ (x – y)j | (1, 1) x = y² y = x² (0, 0)

A: we have to evaluate the following by using greens theorem

Q: The function, r= 3t°, y =ť –t is concave upward on the interval (a) (-∞,0) (b) (0, 0) (c) (-0,0) (d)…

A: The general form of the parametric equation of the curve in two-dimensional space is given by…

Q: ) Verify the continuity of the function f(x, y) 26– 2x -- y at the point (2,-3).

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Q: Let f(x) = x. Show directly that f ∊ R[0, 2]

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Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

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Q: Show that f(x)= |x| is not differentiable at x = 0.

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Q: Let f(x, y) ƒ(2, 1) = = 150 - 2x² - 4y2. Evaluate f(2, 1). Give answer in exact form. 138

A: given  f(x,y)=150-2x2-4y2for  f(2,1) , put x=2  and y=1 in f(x,y)