Show that f1x2 Vin x is right-continuous at x = 1.

Q: is uniformly continuous by definition on the interval (-1,1) . 4 - * Show that f(x) =

A: A function fx defined on an open intervala,b is uniformly continuous on a,b iff  i fx is continuous…

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: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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Q: Use the limit definition of the derivative to compute f'(x) for f(x)= 1/ sqrt of x

A: Given, f(x)=1x

Q: Examine if f(x) = x3sin(1/x) is uniform continuous on the interval (0,2]

A:

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: Find the values of a and b that make f continuous everywhere. x²-4 if x 3

A: If a function is continuous everywhere Then right hand limit and left hand limit on any point will…

Q: The limit as x goes to zero of x-1 exists.   True or False?

A: We need to say whether the given statement, “The limit as x goes to zero of x-1 exists.” is true or…

Q: п-(х-4)" 22и. (2n — 1) Ax) =En=0 n:

A: Solution of given problem as follow

Q: Find the largest open intervals where the function is concave upward. 16) f(x) = x3 - 3x2 – 4x + 5…

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Q: Find where the function is continuous, but not differentiable..

A: Given,

Q: B) Show that fx) = sin for x * 0. for x= 0. X = is not continuous.

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Q: What is the definition of f(x) is continuous at x = a? ||

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Q: Suppose that f (x) < 0 if x is positive and f (x) > 1 if x is negative. Can f be continuous at…

A: f(x) will be continuous at x = 0 if LHL = f(0) = RHL

Q: Show that f(x) = is uniformly continuous by definition on the interval (-1,1) . 4 - *

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Q: Evaluate f (x) = [(3x² + 4x + 3 ) (3x² ) ] at x = 1. %3D Select one: A. Discontinuous B. Continuous

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: find the x-values (if any) at which ƒ is not continuous. Which of the discontinuities are removable?

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Q: If f (s Continuous then on -fex) True or felse?

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Q: Show that f is continuous on (∞ , -∞ )  .

A: we have to show that f(X) is continuous in (-∞,∞). f(x)=x2             if   x<1           x…

Q: Show that the function is continuous on  (∞ , -∞).

A:

Q: Explain why the function ƒ(x) = sin (1/x) has no continuous extension to x = 0

A: Then we can extend the definition of the function at that point to make it continuous there.

Q: Find the derivative of f(x) = x In(x) 1- In(x) O In(x) O1+ In(x) O In(x) /x

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Q: Determine algebraically if f is continuous at x= 0.

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Q: Determine the largest interval over which the fu Vx+2 is continuous.

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Q: Suppose that fis a continuous function and that1. f(x)dx=-1 and L(x)dx = 5, find the value of…

A: suppose that f is continuous function . We have to find the following

Q: Find a function flx) such that f(x) -llex and %3D 3. f(0)-- 주

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Q: Find all values of a and b that make -а - х, x<-2 f(x) = {bx? + 1, Vx+b, -2<x<1 x21 continuous…

A: The function is given by: f(x)= -a-x , x&lt;-2           bx2+1 , -2≤x&lt;1         x+b   , x≥1 Also…

Q: Find the limit as x approaches infinity of f(x) when f(x) is x times square root of x

A: x times sqrt(x)= x times x^(1/2)= x^[1+1/2] = x^(3/2)

Q: Use the definition for continuity to determine whether the function continuous at x= 1 and x= 2?

A:

Q: Where is f(a) not continuous?

A: Given:

Q: Let ƒ be a continuous function. Show that 2022 -f(/¤) dx f(x) dx. 2022

A: It is given that ;  f is a continuous function. And we have to prove that ;    ∫12022-f(x)2xdx =…

Q: 114. Show that if ƒ is continuous, then f(x) dx f(1 х) dx.

A: Proof that if f is continuous, then

Q: Express the limit as a definite integral on the given interval.

A:

Q: Comment on the continuity of f(x) at x = -2, x = 0 and x = 3 If discontinuous, what is the type of…

A: At x=-2, L.H.L.=limx→-2-fx=2R.H.L.=limx→-2+fx=-1f-2=2 Since L.H.L.≠R.H.L., therefore the limit does…

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: find the value of c that make the function continuous

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Q: Is f(x) = √x continuous at x = 0?

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Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: Would it be possible for a function to be continuous on [0,2) but not on [0,2]?

A: Let us consider the function f(x) =(x+4)/(x-2) .

Q: Determine if f(x)=x² is uniformly continous on the interval I = (-∞, +)

A: See the attachment.

Q: Vx + y + 1 f(x, y) ,æ In (y² – x) х — 1 -

A: Given: fx,y=x+y+1x-1,xlny2-x A function f(x,y)=Mx,y,Nx,y is said to be continuous on the points…

Q: what condition when present are sufficient to conclude that a function f(x) is continuous at x=a

A: To show a sufficient condition to conclude that a function f(x) is continuous at x=a.

Q: What are the Continuity Conditions?

A: When a graph has no holes, no asymptotes or the graphs that does not have breaks are called…

Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: is: The interval of continuity of flx) = /2x – 10 OA[5, +0) OB.(-5, 51 OC(-0, + x) OD(-00,-5)

A: Function f(x) is continuous on interval [a,b] if it is continuous at every point.

Q: Show that F(X) = Sin X ornot.

A:

Q: Suppose fx) is continuous on the interval [0,10] and that f(x) = 0 only when x = 4. If f(5)< 0, what…

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