Determine if f : Z × Z → Z is a surjective function if: а) f(m, п) — 2m — п b) f(m, п) — т? — п? - c) f(m, n) = |m| – |n| (here |x| is the absolute value of x) -

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A: To prove this theorem, we use the defination of one one and onto.

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A: Given, f(x,y)=g(u)=x2+y2 To prove that, ∂f∂x2+∂f∂y2=4udgdu2

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A:

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A: Here the objective is to prove that if f is a differentiable function such that

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A: Solution: First, we convert clauses to CNF : (1) ∀xy Fx,y from KB (2) ∀x Fx,Ax (3) Fx,Ax CNF

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A:

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A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

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A: Since the given function is of type function of several variable therefore

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A:

Q: Prove that the function f : R? → R, f(x, y) = sin(/x² +|sin y|) is uniformly continuous on R?.

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

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A: In the given question we have to prove the equation.

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A: Given that f : I → R not be continuous, where I is a closed interval in R.

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A: We have to fill

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Q: Find c such that the function r² – 8 I c T - is continuous everywhere.

A: f(x)=x2-8x≤c8x-24x&gt;c

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Q: (d) Show that the function defined by h: N → N: h(x) = 2*, Vx € N is one-to-one but not onto. Now…

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A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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A: If the given function is continuous at x=a then it is continuous at x=b.

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A: Let's prove this.

Q: Show that the function F: C[0, 1] → R defined by F(f) = max f(x) zE[0,1] is continuous.

A:

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Q: Which f (z) is not analytic at 0 ? 1 f(2) = z + 7 z2 o f(z) = z(z – 4) 1 f(2) = 1 o S(2) = , z-3

A:

Q: Consider the function g : Z × Z →Z × Z given by g(x, y) = (x + 3y, 2x – y). Is g injective? Proof or…

A: The given function is  g : ℤ×ℤ→ ℤ×ℤ given by g(x,y)=(x+3y, 2x-y).

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A: Given: The given fx=x3+x2+2, x0=1,h=0.5,x1=1.5 and x2=2

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A: Given that, f1x=4x-3x≤1-3xx2-4x&gt;1f2x=1+2+x2 To determine set of points which they are derivable…

Q: Let F = (2y? + z)i+ 4ryj+ æk. (a) Show whether F is conservative.

A:

Q: Let f : R? → R² be defined by f(x, y) = (x – 2y, xy). Prove that f is continuous at (1, 1).

A: Let f:R2→R2 be defined by fx,y=x−2y,xy We have to prove that f is continuous at 1,1. For continuous…

Q: t. Ost<1 f(t)={-1. 1st<2 -t, 2sts10

A: Topic = Functions

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A: We have to prove that   √a+√b≤ √(a + b) for all a, b ≥ 0.

Q: Consider the function g : Z x Z → Z × Z given by g(x, y) = (x + 3y, 2x y). Is g injective? Proof or…

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Q: الموضوع Let f be a function de fined by f xE Q if XE Q Prove that fis cont but not de.

A:

Q: 36. f(x, y, z) = vy – x² In z

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A: Given,