If |fn(x) – fn(y)l < M|x – y|ª for some fixed M and a > 0 and all x, y in a compact interval, show that {fn} is uniformly equicontinuous.

Q: 'he function f: E → R is uniformly continuous if

A: We have to find the answer using the definition of uniform continuity.

Q: Let f (x, y) = 1 5+√x²+y²-1 Then range of f is:

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Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

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Q: Show that f[x0, x1, x2] = f[x2, x1, xo].

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Q: Let f [0, 2] → R be a continuous function, with ƒ(0) ≤ f(1) ≤ f(2). Show that there : exists xo [0,…

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Q: Let's assume that f(x)= r²+c* I c-16 g(x, a) = a* x² + ar Find a such that the following error is…

A: Given that where            That is  Also, given that

Q: Determine the largest subset S of C where the function f(z) = 3x2 + 2x - 3y2 - 1 + i(6xy + 2y) is…

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Q: If X is uniform in the interval [-3,3] compute X(i.e. E{X}) and o² (i.e.E{(X-X)²}).

A: Given that X ~ U[-3,3] to find mean and variance

Q: Let f = {(1,1), (2,3), (0, –1), (–1, –3)} be a linear function from Z into Z. Find f(x)

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Q: Find the absolute maximum and minimum values ​​of f (x, y) = x² + 2y²-x in the set D = {(x,y) ∈ R²…

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Q: Show that f: R\{2} → R\{5} defined by f(x) = (5x+1)/(x - 2) is bijective.

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Q: How many functions f:R→R  exists such that : 2f(x)+2f(y)=f(x+y)+f(x−y)+2y holds for all real x and…

A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

Q: 6. Prove that |xy| = |x|ly| for all real numbers x, y.

A: The given problem is to prove the following statement. Given statement is |xy|=|x||y| for all real…

Q: Prove, if f(x)= V1+x² –In +1+ 1 is increasing and concave on x X E (0;+∞) .

A: f is increasing if first derivative is positive in the interval  and f has concave if second…

Q: 6. Prove that f(x)=√x is continuous for all x ≥ 0.

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Q: Verify that ||v-w||^2=1 when ||v||=2, ||w||=1, and v*w=2

A: By the definition of inner product and norm we can derive the following formula : ‖u-v‖2=⟨u-v,u-v⟩…

Q: Compute f, fy, f fy, and fr of the function. f(x, y)=(2x-3y)* |

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Q: -2 x<-1 Q1)a) For what values of a and b is g(x) = |ax - b - 1<x< 1, 3 x21 Continuous at x=1

A: From  the given problem:   gx=-2x≤-1ax-b-1≤x&lt;13x≥1     As we know that a function f(x) is…

Q: ) Let f: R → R be defined by f(x) = 5x³ – 7x – 10. Prove that if |x| ≤ 3, then |ƒ(x)| ≤ 166.

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Q: 3. Let f A B be a function, and let Ao C A, BoC B. Prove that (a) f(f(f(Ao))) = f(Ao); (b)…

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Q: Find f(2021) if the function f satisfies following conditions: f(1)=1 f(x+y) = f(x) + f(y) for all…

A: take 1 for x and 1 for y  f1+1=f1+f1 f2=2 similarly, substitute 2 for x and 1 for y f2+1=f2+f1 f3=3…

Q: 3x +1 III.(10) Prove that the function f: R – {5} –> R – {3} defined by f(x) = is a bijection. x- 5

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Q: Suppose f is a differentiable function on an interval II and f(x) 6= 0 for every x in the interval.…

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Q: examine the continuity of the function

A: Given function is not defined at x=0

Q: Find the values of x for which the gradient of the tangent to the graph of y=f(x) is equal to the…

A: We have to find the values of x for which the gradient of the tangent to the graph of y=f(x) is…

Q: 6) Let F(x,y,z) = and f(x,y,z)= || F(x,y,z)||. Show that V(Inf) = F/f².

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Q: 2. Let X - Uniform[0, 1]. Calculate E(E(X)) and Var(Var(X)).

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