The function h(x) = sin væ² + 1, x E R is continuous on: O R\{-1} O R\{-1,1} O R\{0} O R O R\{1}

Q: xy' - y = = x tan Y 18

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Q: 2. Consider the function / with domain (-2, o0): 3|2 – 1| 2 + 27 - 4 if – 2 <z<1 f(z) = if r = 1…

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Q: Find all differentiable functions f: R→R such that f'(x) = F(x + n) – f(x) n for all real numbers x…

A: As f'(x)=f(x+n)-f(x)n is true for all positive integers values of n thus substitute 1 for n in…

Q: the function f is not differentiable at x=0.

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Q: -1+x+ 4x² cos (4) når r + 0 når x = 0. f(x) = %3D %3D

A: We have given function;

Q: is The functionFIO-Vx4iscontinusus onR. It cosă

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Q: 3. Consider a function f(x) = sin() : R → R. x²+1 (a) Show that f is continuous on R.

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Q: b) Give an example of a function g: R →R that is continuous at some xE R, but not differentiable at…

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Q: 2. Determine if a function f : [0 ; 2pie] → R defined by f(x) = sin 2pie is continuous

A: Determine if a function f : [0 ; 2pie] → R defined by f(x) = sin 2pie is continuous.

Q: Describe the continuity of the function h in the interval [0, π]. Show solution and explain

A: Given Function, hz = ez sin z - sin z + cos z, Given interval : [0, π ]

Q: If f is an entire functions then h(z) = e² f(1/2²) is analytic on C\ {0}, and its derivative h'(2) =…

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Q: Let f be continuous on the interval [0, b], where f(x) + f(b − x) ≠ 0 on [0, b].

A: Let I=∫0bfxfx+fb-xdx   I=∫0bfxfx+fb-xdx                     ....... (1) use ∫0afxdx=∫0afa-xdx…

Q: Q: Show that the function f(x)=- x sin ,X =0 is continuous at x = 0.

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Q: The function f (x) = x sin is continuous on the interval (-1,1). O True O False

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Q: Consider the function f: RR defined by f(x) = 0 if x is irrational and f(x) = 1 if x is rational Is…

A: Note: f is said to be Riemann integrable on [a, b] if To Prove Dirichlet's function which is defined…

Q: By, Where F(2, y, z) = sin yi+(2 cos y+cos z)?+y sinză und (sint, £,2),0 < t < 2

A: Value of the line integral

Q: Define S = Qn [0, 1] and the function f: SS that satisfies f(0) = 0 and when p and q are 1 coprime:…

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Q: sin () if x + 0, COS X Let f : R → R be the function given by f(x) if x = 0. -1

A: The function  f:ℝ→ℝ is defined as follows: fx=sin1xcosx  if  x≠0-1                    if  x=0…

Q: Find the continuous lest squares approximation of degree 2 for f(x) = cos(xx) on [0,1]. %3D

A: Let P2(x)=a0+a1x+a2x2 is the continuous least square approximation of degree 2 for the function…

Q: |Consider the function f with domain (-2, 0): 3|1² – 1| 21² + 2r – 4 if – 2<1<1 f(z) = if x = 1 3 if…

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Q: If fis a bijection, find the sets X and Y.

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Q: - {2²2 (sin + cos2) z € (-1,0) U (0,1] 0 x = 0. f(x)=

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Q: Find the range of the function R → R Define by f(x)=(tan. 'x)* V1+x? 2 +

A: Range of bothe functions will be considered and then intersection of both we have to take.

Q: Prove that the function f(x)=sinπ|x| is continuous at x = 0 but not differntiable at the same point.

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