Are the following functions continuous? Explain X, x < 1 f(x) = x2. 1 < x x < 3 g(x) 3 < x

Q: Determine whether function is continuous and/or differentiable at x = 1. f (x) = 1/x

A: Consider the given function fx=1x

Q: Describe the interval(s) on which the function is continuous. f(x) = (x + 1)/√x

A: We can not have negative number inside the square root.  So, x≥0   And we can not have 0 in the…

Q: Consider f(x) = x6/5. Is f(x) differentiable at x=0? Is f(x) continuous at x=0?

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a.…

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Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

Q: is the function f(x) = 1/(x-2) continuous on [1,3]? Justify your answer.

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

A: Given: fx=xx+3

Q: Is the given statement true or false? Justify your answer. 'If the function f is continuous at a,…

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Q: Determine if the function f below is continuous at x = 1: [1– VI– x, x 1

A: We have to find

Q: Are the following functions quasiconcave, quasiconvex, both, or neither: f(x) = x³ - 2x f(x₁, x₂) =…

A: Please comment if you need any clarification. If you find my answer useful please put thumbs up.…

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

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Q: ( 2x -. Is g(x) continuous at 2?

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Q: - Show that f(x) is continuous at x = 1. f(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: Assume that F and G are differentiable functions such that F (x) = -G(x) and G (x) = -F(x) . Let…

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Q: 71. Is the function given by g(x) = 4x - 6x continuous on R?

A: To check whether the function g(x) is continuous on ℝ. The given function is gx=4x3-6x Also, the…

Q: ecos-1 x if x 1

A: If a function has to be continuous  then it must to follow below Left hand limit = Right  hand limit…

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

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

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1+ (F(x))*. What is…

A: Given that f(g(x)). = x  and f'(x)= 1+(f(x))2 and we find g'(x). Here i attached solution of this…

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

A: We need to check the continuity of the function

Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

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Q: Is the function f (x) below continuous on [3, +00)? (0, x > 0 X, 0 3

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Q: Consider a continuous function f(x)=2ex−1−2x. The graph of f is decreasing on which interval/s?

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Q: what is the mathematical condition for the function to be continuous at a certain point c?  is the…

A: A  function is said to be comtiuous at a point x=c , in its domain if the following three conditions…

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: Describe the interval(s) on which the function is continuous.                            f(x) =…

A: fx=xx2+x+2 Since there is no common factors in the numerator and denominator, therefore there is no…

Q: Determine whether the function is continuous at the given points. x+2 if x22 : 2,0 x if x<2 f(x) =…

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Q: Is f continuous at x = 3? Explain why or why not. f(x) = √1+x for 0≤x≤3 f(x) = 5 - x  for 3<x≤5

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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: x +1 x 2

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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: g(x) = sec(x) %3D

A: To find all the intervals the function g(x)=sec(x) is continuous

Q: Let f be a function that is continuous on the closed interval [1, 5] with f ( 1) = 10 and f (5) =…

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Q: Is the function given below continuous/differentiable at x = 3? %3D -3x + 2 x 3

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Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: Is f(x) = √x continuous at x = 0?

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Q: 4) Is the following functions continuous? for x < 1, d(x)= x- 2 for 1 < x.

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Q: Redefine the function f to make it continuous at x = 0. -8x + 36 + x (х — 4) ; x + 0,4 f(x) = 4; x =…

A: Consider the condition for continuity.

Q: Is the given statement true or false? Justify your answer. 'If the function f is continuous at a,…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: 1. Explain what it intuitively means for function f(x,y) to be continuous in some domain D.

A: To explain the meaning of the given statement.

Q: 3. What value of k would make f (x) continuous at x = 3 ? 3.

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Q: h(x) = x+1 %3D at x = 1 x2-1

A: Function f(x) is continuous at a point x=a :Function should be defined at x=a, and  limx→a-f(x) =…

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: Find a value of k making h(x) continuous on (0, 5). 0 < x < 2 2 < x < 5 h(x) = x +1,

A: A function is continuous if limx→a+ h(x)  = limx→a- h(x) = h(a) Now in the given question, function…

Q: For what value of a is the function continuous at every x?

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Q: On what domain is the function f(x) = 5+ V2x + 6 continuous? %3D

A: Let's find.

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.