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A:

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A: As per our guidelines we are supposed to solve only one question i.e. the first question. For the…

Q: (0,1). Prove the following functions is uniformly continuous on sin x f(x) =

A: Uniformly Continuous:-  Here we prove the result using a theorem of uniformly continuous.

Q: Hello! What is the solution to this question? Thank you for your help! Have a nice day :)

A:

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A: We have to apply the comparison test

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Q: 6. If f is continuous and f(x)dx=4 , '3 | xf(x?)dx=

A: Explained below

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Q: If f : [0,2] → R is defined by f(x) = 1 if 0 ≤ x ≤ 1, f(x) = 2 if 1 < x ≤ 2. Show that f is…

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Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

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A:

Q: 3. Find a value of b so that the function x 1 f(x) = is continuous on (-0, 0).

A: A function is said to be continuous if Left Hand limit = Right Hand limit = f(a) In this question,…

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A: We have to find

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A: Given that, 2x-y=3+cosy Also 2x-y=3+cosy is continuous on 2,2.1 and differentiable on 2,2.1.…

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Q: Suppose f is continuous on the closed interval [-1, 3]. If F is an antiderivative of f, which of the…

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Q: f(x)dx converges then lim,f(x)=0

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Q: Question 6. For what value of b is x, x -2 continuous at every x?

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Q: 43. Let f(x, y) = Is it possible to define f(0, 0) so x² + y2 * that f will be continuous at (0, 0)?…

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Q: 4 – x² p(x) = x – 1 at x = 0 Select the correct response: Continuous O Discontinuous

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Q: 5. Let X-f(x; 0) where f(x;0) =exp{-lx-01}(-m)(x), 0 E R. Find the MLE of 6. %3D

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Q: (x²-x for x +0 If f(x) : and if fis continuous at x = 0, then k= 2x f(0) = k -1/2 O 1/2 O 1

A: f(x) = (x2 - x)/2x limx→0 x2-x2xlimx→0 x(x-1)2xlimx→0 x-12= -12

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A: This is a problem related to derivative of the function. Based on the general formula and concept we…

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Q: If f(x) is a strictly increasing continuous function with domain [0, 00]. If f3(x) = tf()dt. 0, Find…

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Q: a. Find the value of (k) that make the fumction flk) = ,continuous atx = 0 +3k-3 x=0

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Q: 4 Suppose that f is continuous function such that |F( x) # x and 4 [(4x)dx = 3. Then fxf(4x² )dx =?…

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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…

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Q: 1+ cx, if x 2 Given the function: f(x) = C - x, What should be the value of c so thatf is…

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Q: 2 If f is continuous on [0, 2] and f(x) dx = 5, find the value of | f(æ – 2) dæ.

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Q: Suppose f is a differentiable function with f(7)=1 and f '(1)=- Let y= f(x)·tan x+e* •cos x . Then…

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Q: 3 - x, x<2 Q.No.15: Is f(x) = {+2 x22 continuous at every x € R. x+1 xs1 -.

A: Continuity of a function.

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A: Given  f(x)=3x2-1if x&lt;0cx+dif 0≤x1x+8if x&gt;1

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Q: 3. Let f)=x+x+2x-1E2,lx). Then x= 1 is a root for r() of mmltiplicity 3D1 None 4 2

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A: Given that for x&lt;=0, F(x) = (x - 1)/4 Then as x tends to zero from the negative side of zero, we…

Q: 3. Consider the function g(x) defined by { x² sin(1/x) if x > 0, g(x) = if x <0. (a) Show that g(x)…

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Q: a non zero valie for the constant k that makes the fmction ww m tan(kx) x< 0 f(x) = 3x + 2k?, x 20…

A: To find a non zero value for the constant k that makes the function…

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A: Here given function is continuous and strictly increasing function on [0,1]

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Q: The Gamma Function is defined by [(x) = fx-¹e-tdt, positive integer then prove that for na T(n) = (n…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.