Let f function from (N,d ) to (N,d ) defined as f(x) = x , where d usual metric, then f is continuous at every points O continuous only at x=10 continuous except at x-1O discontinuous at every points

Q: 10. If a € Z, then a³ = a (mod 3).

A: To prove that for any integer 'a', , we need to show that  and a have the same remainder when…

Q: 7. Let f, g: [0, 0) → R be continuous on [0, ∞) and differentiable on (0, o0). If f(0) = g(0) and…

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Q: Suppose f is a function defined and continuous on the open interval (a, b). Suppose g is a function…

A: Given that: f is a function defined and continuous on the open interval (a, b).g is a function…

Q: p) State Cauchy's Schwarz Inequality and prove this for Space of Continuous functions on[-n, n].

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Q: Show that A Function with a Single Point of Discontinuity 2xy x² +1,²² 0, is continuous at every…

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Q: (6) Are all continuous functions on ID differentiable on D?

A: we have to identify the given statement is true or not

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

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Q: (((I) The function must be continuous at that point I) The limit of the function at that point must…

A: Please see the below picture for detailed solution.

Q: A) If g'(x)>0 for all x in the interval (4,7) then g(x) is for all x on the interval (4,7).| B) If…

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Q: Define. Show that h is continuous at x = 0 but h' (0) does not exist

A: Function is said to be continuous at a point x=a, when the function is defined at a and the limit of…

Q: Determine whether the statement is true or false. '8 If f'is continuous on [7, 8], then f '(v) dv =…

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Q: Is a function Continuous ?why? integrable anod

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Q: ·b f(b) − ƒ(a) = f'(a)(b − a) – ſå ƒ"(x)(x − b)dx - a

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Q: Let /: X →Y be a function, A, BC X and C, DCY. Show that: 1. f(AUB) = f(A) uf(B) 2. If AC B, then…

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Q: Find all points of continuity of f(x,y) = ( y* (sqrt(x^2+y^2)) / |y| If a) y does not equal to zero…

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: Determine the set of points at which the function is continuous. if (x, y) # (0, 0) 5x? + y? f(x, y)…

A: We know that given function is continuous in its domain so we need to check only at point where…

Q: 2. Determine the points where f is continuous where x + Y if (x, y) # (0,0) f(x, y) = x2 + y2 if (x,…

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Q: Let & be continuous in [a,b] and differentiable in (a,b). It's true that: a) f (a) = f(b) = 3 x €…

A: Statement (a): f(a)=f(b)  implies there exists x0​∈(a,b)  such that the tangent line to the graph of…

Q: Use the definition of the derivative f'C)=lim flxty-PG4. to compuke derivative of flx)= 3X-X

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Q: Prove that f(2) = z/(z* + 1) is continuous at all points inside and on the unit circle Iz] = 1…

A: we need to find those points where the denominator ( z^4+1) equals to 0

Q: Show that a uniformly continuous function on (a, b) is bounded.

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Q: 2) Consider the function f defined as: 3x f(x)=sin(x)' 2x + 3, a) Is f continuous at x ==? Explain.…

A: The given function,The aim is to find the following,(i) Check continuous at .(ii) Check…

Q: If f is a continuous function on [a, b], ƒ is differentiable on (a, b), and if both f(a) and f(b)…

A: This question is based on Rolle's theorem which is explained in step 2.

Q: Let f be continuous over [a,b] and differentiable over (a,b). Then there exists at least one point…

A: Let f be continuous over a,b and differentiable over a,b. Then there exits at leastone point c∈a,b…

Q: Q\ Use appropriate functions to guarantee that (). x sin if x # 0 h(x) = 0, if x = 0 is continuous…

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Q: If f is a continuous function on [a, b], and if f (a) = -2 and ƒ (b) = 2, then there exists a real…

A: Hi, you can find the answer in the handwritten form.  Given f(a)=-2  f(b)= 2

Q: If f', and y are continuous on [a, b] and derivable on Ja, b[, then show that there is a value c…

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Q: 3. Define f(x) so that S(2) = {ap(). f(x) = 0, |피 1 (a) Explain why the function f(x) must be…

A: As per our guidelines we can answer only 3 subparts. please ask others seperately.

Q: Let f : [0, 1] → R be a function with Darboux’s property such that for any y ∈ R, the set  f…

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