Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5? Why or why not?

Q: By considering different paths of approach, show that the function f(x, y) has no limit as (x, y) →…

A: Let S be an open set containing , and let f be a function of two variables defined on S, except…

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

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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: 2. When can we say that a function is continuous at an interval?

A: We know that when a function does not have any discontinuity, then it is a continuous function. It…

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

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

A: Given that,

Q: (-х+а, х < —1 If f(x) = {x² + 5, –1 < x < 2 is continuous then х — b, х 2 2 a + b =?

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Q: When is a function continuous over a closed interval?

A: A function is continuous over a closed interval when it is defined at all points in the interval…

Q: Suppose that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. What is the value f(2,…

A: Given that f(x, y) is continuous at (2, 3) and that f(2, y) = y3 for y ≠ 3. We have to find the…

Q: Find f(2) Is f continuous at x = 2? Explain your answer.

A: Given function

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 x - 2 ax2 - bx + 3 if x < 2…

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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: Describe the interval(s) on which the function is continuous.

A: Given: Describe the interval(s) on which the function is continuous. f(x)=sec πx4Clearly from the…

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) = if 2 < x…

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

A: Given,

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

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Q: 4. Is the function f integrable over the interval [-4,1]? Briefly justify your answer. 2x2 + 5x – 3…

A: Solution  Question 4  Given,  fx = 2x2+5x-3x+3  We have to find the function is integrable in the…

Q: Jaimie, a MAT student, claims that "For a continuous function f(x), defined on an interval [a, b],…

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Q: Determine whether the following function continuous at point (1, 1). Justify your answer. (x²-xy if…

A: Here we have to determine whether the given function is continuous or not.

Q: (2) Are all entire functions differentiable on D?

A: Here we check whether given statement is true or false. Are all entire functions differentiable in…

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

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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 values of a and b that make f continuous everywhere. x² – - 4 if x < 2 X - 2 f(x) ax2 - bx…

A: Please refer the attached image for complete solution.

Q: By considering different paths of approach, show that the function f(x,y) has no limit as (x, y) →…

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Q: Describe the long run behavior of f(x) = x* As x → ∞, f(x) → ? As x → 0, f(x) → ?

A: This question is about function behaviour near infinity

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: The function f(x)=³ in (x) is continuous everywhere except x (х-1) at x=0 and at x=1. When…

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Q: When can we say that a function is continuous at a number?

A: To explain: The continuity of a function at a point.

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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Q: Suppose f is a f(8(x))=2x² and differentiable function where 2x f'(x)=2+ f (x). Show that g'(x)=…

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Q: Please show all work:  Is f(x)= x2+3 continuous at x=1? Why or why not? (A rigorous mathematical…

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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: Where is f(a) not continuous?

A: Given:

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

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Q: Suppose that f: R² R is a function given by y³ x² + y² f(x, y) = 0 for x = y = 0. Show that f(x, y)…

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Q: find the value of c that make the function continuous

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Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Determine whether the function shown is continuous over the interval (-5, 5).

A: We will determine whether the function is continuous over the interval (-5, 5) as following.

Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

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: d photo continuous and differentiable

A: The given piece-wise function is,  f(x)=12x+18if x&lt;66x+15if x≥6

Q: 8) Assume that 2 + Va if x >1 if x < 1 f(x) = Determine whether or not f is continuous at x = state…

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Q: Show that x³, if x 0 is not continuous at x = 0. %3D

A: According to the problem, we have

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: Does f(x) 1-V1-x² continuous on the interval [-1, 1]?

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Q: If f(x) is continuous at x = c, then so is If (x)|.

A: To determine: The given statement is true or false. Given statement: If f(x) is continuous at x=c,…

Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

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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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