Explain why or why not f(x) is continuous or not continuous at x = 1 using the ideas of the delta epsilon definition. f(x) =- if x 1 x-1 a 2 if x=1

Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: 4. h(x) = x-T at X %3D 2. 5h(X) = x + x4-1 at X = %3D

A: Continuous function at x=a

Q: g (x) = In tdt %3D 1 Is this function is continuous everywhere. If not than where it's not…

A: see below the answer

Q: If the product function h(x) = ƒ(x) . g(x) is continuous at x = 0, must ƒ(x) and g(x) be continuous…

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Q: If f is continuous on [a, b] and "If(x)| dx = 0, what can you conclude about f ?

A: Solution:Given If f is continuous on a,b and ∫abf(x) dx = 0To conclude about f ?

Q: (tan ) 1/x TC + x 4 * f(x)D. k, For what value of k, f (x) is x =0 continuous at x = 0?

A: The

Q: If f is differentiable at a number, x, then f is continuous at x.

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Q: 1. What is the definition of what it means for f(x) to be continuous at x = a? Discuss the ways that…

A: In this question, we need to define the meaning of f(x) to be continuous at x=a and different ways…

Q: If f(x) is continuous at x=a , then f(x) is also differentiable at x=a.

A: " If F(x) is continuous at x=a then f(x) is differentiable at x=a." The condition for the function…

Q: 25 If f is continuous and f(x) dx = 8, find xf(x²) dx.

A: given ∫025f(x)dx=8∫05xf(x2)dx=?

Q: Suppose h' is continuous x>0. IF x = 0 and h'(x) = 3√tan (2x)-1 it exists. i at Find h (0), 'F

A: For the solution of the problem follow the next step.

Q: Suppose f is a continuous function such that Si f(t)dt = e® In(x) for all x > 0. What is the value…

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Q: If f(g(x)) is continuous at 0, then g(x) is continuous at 0  true or false

A: Given that If f(g(x)) is continuous at 0, then g(x) is continuous at 0

Q: Suppose that f(1) = 3, f(4) = 5, f '(1) = 4, f '(4) = 4, and f " is continuous. Find the value of xf…

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Q: Suppose that f(1) = 4, f(4) = 5, f '(1) = 6, f '(4) = 3, and f " is continuous. Find the value of xf…

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Q: Suppose f is continuous on [0, 1]. What is lim n→ ∞ 1 S fo 0 f(x) dx?

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Q: If ƒ is differentiable at a, must ƒ be continuous at a?

A: we know that for a given function if it is differentiable at given point then it must be continuous…

Q: Suppose that f (x) is a continuous function, f(-1) = 6, f(2) = and f(x)dx: = -3 = T. Evaluate the…

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Q: Suppose that a continuous function g satisfies: g(x)dr = 30 and g(2x)dx = 3. 0. 2 Find r9(3x²)dx.

A: Suppose that a continuous function g satisfies: ∫03gxdx=30 and ∫06g2xdx=3. The, we have to find the…

Q: B) If f is differentiable at x, then prove that f is continuous at x Is the converse true? Why

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Q: Let X be continuous with pdf f(x) = 3x² if 0 <x< 1, and zero otherwise. Find: (a) E(X). (b) Var(X).…

A: The pdf of X is given by f(x) = 3x2 if 0 &lt; x &lt; 1 Note : According to our guidelines we are…

Q: Suppose that f (x) > 0 for all x, f(x) has a continuous derivative and that е — 1 f(-3) = 0 and f(4)…

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Q: Is the function continuous  f(x) = e^x / 1 - e^x

A: We need to check the continuity of the function

Q: . Explain why f (x) = sin (x² + 3r + 1) is a continuous function for all c eR.

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Q: Let f(x) = CX– 2, x > I lx+ 8, x < 1 For what value of c is f(x) continuous on (-00, 0)

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Q: Show that the function is continuous. f(x) = cos(x 2)

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Q: Suppose that f(1)=8, f(4)=−4, f′(1)=−3, f′(4)=2, and f′′ is continuous. Find the value of ∫from 1 to…

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Q: Show that the following function is not continuous at (0,0). { 3 x2+y6, 0, , if (x, y) # (0,0); if…

A: To prove that given function is continuous. gx,y=xy3x2+y6,   if x,y≠0,00,              if x,y=0,0

Q: True or false: if f(x) is continuous at x =a, then f(x) is differentiable at x =a.

A: We have to determine the given statement as true or false.

Q: Show that the function is continuous over ]-infinity, +infinity[ 4 x* sin(1/x) si x#0 f(x)=: si x=0

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Q: If a function f(x) is not defined at x-a, then it is not continuous at x-a.

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Q: Show that the function below is continuous at x 0 (cos x-1 f(x) D if x<0 5x, if x20

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Q: show that f,given by f(x) x +0 )is continuous on R-{0}

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Q: b) Show that the function f (x) = { * x² sin ! for x E (0, 1] for x = 0 is absolutely continuous on…

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Q: Show that the function f(x) = csc(x) is not uniformly continuous on (0, pi/2]

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Q: 10 If f is a continuous function and F(x)=f(x) for all x€R, then | f(Gx)dx=?

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Q: Determine if the function f below is continuous at x = 1: ſ1– VT- x, x 1

A: According to question,given function,fx = 1-1-xx≤1ln xx&gt;1

Q: continuous at (C

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Q: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

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Q: 87. If f is continuous and f(x) dx 10, find f(2.x) dx. %3D

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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: True False Suppose f(x) is differentiable at x=a. Then f also continuous at x=a.

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Q: If f(z) is continuous at z then it must be differenttiable at z, 0.

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Q: . Is f(x)= Vx + 1 continuous at x == -1? Yes, because all functions are continuous No, because the…

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Q: 6. gx) VX- 3 at x = 4 三 7 g(x) at X = 8 三 e1 gCX)= n4ーメ at x =0

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Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

Q: The function f (x) ,x € [-27, 2n] is continuous on: 1-cos x

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Q: Find the value of fa) which makes f(x) continuous at x = a (if exists) where X - x f(x) a =

A: Given function is fx=x-xx Find the value of fa=0.

Statements and Logic

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