22. (a) Prove that [0, x] = [0, y] for all x, y E Z, x + 0, y # 0. (b) Prove that [ax, ay] = [x, y] for all a, x, y E Z, a ± 0, y ± 0. (c) Prove that [x, x] = [1, 1] for all x E Z, x + 0.

Q: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). Which of the…

A: Given: Suppose that Q(x, y) is a function such that 1/Q(x, y) is continuous for all (x, y). To Find:…

Q: (x+1)+-y² Suppose g(x, y) = {(x+1)++y² ' (-1, if (x, y) + (0,1) if (x, y) = (0,1) Find g,(0,1) and…

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Q: Assume that all functions are continuous on some interval (a, b). Prove that if y₁ and y2 are…

A: Since we are given that y1 and y2 are solutions of the differential equations  y' + p(x)y = f1(x)…

Q: Q1) Find the canonical form of these question : a) f(x.y,z) =F=x' y' z+x y° z" +x y z b) f(x.y.z)…

A: We are given: f(x,y,z)=F=x'y''z+xy''z''+xyz We are given the standard Form. F=x'y''z+xy''z''+xyz…

Q: d g(s) be two differentiable functions in R and f  (2) = 8, g(2) =0, f(4) = 10 , and g(4) = 8 Then…

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Q: t f(x+y)=f(x)+f(y) + 2xy-1 for all real x and y and f(x) be a differentiable function. [f f^ prime…

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Q: Find V· (V × F), if F(x, y, z) = 3e**i+3xe'j – 3e²k. - V·(V × F)

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Q: If f(x,y) =log, (cos (e* ))+ sin(x + y) then f (x,y) is ây ôx A) – sin(x + y) B) 0 C) cos (x + y)…

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Q: 0, x<0, F(x) = { 공x?, O<x<2, 1, x22 a) Find E[X]. b) Find P(X 21|X)

A: From the distribution function we get:f(x)=ddxF(x)=ddx14x2=x2 for 0≤x&lt;2f(x)=0 otherwise. So,…

Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: (6) . that Let f(x) be a differentiable function on the interval (0, 0) such f (x*) = 3f(x), for…

A: We have to prove the given equation.

Q: Display the discontinuity of h at (0,0) and Evaluate hx(0,0).

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Q: 1. Consider the function y = f(x) displayed below. y 3 это 5 (a) For which values of x in the open…

A: Let's analyze the function y = f(x) displayed in the graph and address each part of the question:(a)…

Q: Q3. Find y= fx) such that y

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Q: Let f(x)be a function on (0, 0) satisfying the following: f(x) > 0 on the interval (0, o0) f'(x) > 0…

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Q: 4. Let f(x, y)=2x*y' . Find f,(x,y)

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Q: Let f(x + y) = f(x) f(y) for all x and y. Suppose that f(3) = 3 and f'(0) = 11, then f'(3) is given…

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Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: Let f(u) = u* and g(x) =u = 2x* + 6. Find (fo g)'(- 1). (fo g)'(-1)= (Туре an exact answer.)

A: Given:- Let f(u) = u4 and g(x) = u = 2x4 + 6   To Find (fog)'(-1).

Q: Q: If f(x)= ax* + withE a, > 0, b >0 +b,x + b, then show that Lt f(x)=o ifn>m. %3D

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Q: Let a be a real number and f(x, y) = 5ax?y+ 5xy³. Let v = 3i – j and let Vf(x, y) denote the…

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Q: Let a(t), 2 < t< 8 be a positive function. Also, let the function 8(t) be defined as a'(t)/a(t) on…

A: We will find out the required expression.

Q: Let g(x) = 2 f(u) + 3 where . u= u = with respect to x? ○ 2. f' (u) +3 O (2. f' (u) + 3) (2x + 2)…

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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: 2. At what points of R² is the function continuous? (sin(x² + y²) x² + y² f(x, y) = 0, -, if (x, y)…

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Q: X Let f(x,y) = 8 e + In (x+y). Find the following. (a) f(1,0) (b) f(2, -1) (c) f(0,e) (d) f(0, e 4)…

A: Note: According to our expert guidelines only first three subparts are to be answered kindly repost…

Q: Let f(x)be a function on (0, o) satisfying the following: f(x) > 0 on the interval (0, o0) f'(x) > 0…

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Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: Let f(æ) = (x – 9)* – 5, determine f-(x). f\(x) =|

A: We need to find inverse function.

Q: (3) Let f : R –→ R be a differentiable function everywhere. Prove that if f (x) = 0 has n solutions,…

A: