32 Show that d(KA) is uniformly. Continuons it A is any subsxt a motric space X. of b) Show that d (X,₁A) 0 for all x& A if A is closed

Q: Prove that if ƒ and g are Riemann integrable on [a, b] then fg is also Riemann integrable on [a, b].…

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Q: 4. Let X₁, X2,..., XnEX and r> 0, for i = 1,2,3,...,n. Show that U=1 N (X) is bounded.

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Q: Define fi z-> 2 xZ by Ala)l (2,72t1) if xis even 18,0) if t is odd a) Is f injective 2? b) Is f…

A: We have f:Z→z×z Such that fx=x,x+1     if x is evenx,0          if x is odd

Q: Show that F(x, y) = x² + 3y is not uniformly continuous on the whole plane.

A: Given that function F(x, y) =x2 +3y We have to show that it is not uniformly continuous on whole

Q: 4- If a function is differentiable at zo, then it is : a) Differentiable on C b) Continuous on C c)…

A: To answer the given question about the complex function.

Q: Indicate whether the following statement is true or false. Let f(x, y) be any c' real valued…

A: Given fx,y be the C1 real valued function defined on the rectangle R=a,b×c,d. Then we have to check…

Q: 2. Let f be defined on an open interval (a, b) and assume that for some e e (a, b) we have f'(c) > 0…

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Q: f(z) = Im z is continuous 0 صواب ihi O

A: True

Q: 2. !. (n!)². > Show that there is no holomorphic function f (z) on any open set containing 0 such…

A: To Prove: There is no holomorphic function fz on any open set containing 0 such that fn0=n!2.

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Q: * The statement : Every bounded real valued function over [a, 6) is Riemann integrable over (a, b)…

A: Necessary condition for a function to be Riemann integrable is that function is bounded and interval…

Q: A ve B iki küme, f : A → B bir fonksiyon ve X, Y C A olsun. a) f(X) – f(Y) C f(X – Y) olduğunu…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 7.2 Give an & - 8 pr at (1 continuous (2x - 2).

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Q: Q3) if the continuous function is : 4x+1 F(x) -+k at x= h. Find the value of h,k.

A: 3). Given function is:   fx=4x+1x<hx3+kx=hx2+1x>h Solution: A function fx is continuous at x=h…

Q: Let f(x) = x -[r] and f :[1,5) →[0,1). What is the discontinuously type of f(x) at the point x = 3?

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

A: The suitable formula for continious       LEFT HAND LIMIT = RIGHT HAND LIMIT

Q: 14. Let f be a continuous function on R2. Consider p2r+2 f(x,y), I = o Jr+1 -dydr I+1 If taken x = u…

A: Ff

Q: Suppose that fand gare continuous functions such that f(z)dz = 2and s(z)dz = 3, find (2f(2) +…

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Q: 5. Determine the vclue of c such that the function is continuous on (-o0,00 + flx) = 2x, x SC

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Q: Suppose f ond 9 are continuous functions on [0. b] ond thand gee)>0 for all x E [0,b]. Prove that…

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Q: the 18) use definition to deformine whether or not given functions are uniformly continuous a) for X…

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Q: el 29-38 Determine the set of points at which the function is continuous. 29. F(x, y) = xy 1 + e*- 1…

A: Solution:

Q: Ex L: =)(co(ax) – 7sin(3 x)) FC<). gC<)dx Let V be the vectar real valued function of all continous…

A: An inner product space is a function from a vector space to another vector space. There are certain…

Q: 22) Lee f be a contioouse function on the closed ineerval [-S,0], where f(-51=0 and rco)=5 which of…

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Q: 3. Let fx) = {ax), whire a function. sadafferentiable 10 94x) 1t xa aa glx) and a'cx) Lalwlate the…

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Q: 3- i) Let f: A→B and g: B-C. If gof is one to one (1-1), then show that f is one to one. ii) Let h:R…

A: Injective Function.