Determine the interval(s) on which the following function is continuous. At which finite endpoints of the intervals of continuity is f continuous from the left or continuous from the right? f(x) = 6x2 - 108 The function is continuous on the interval(s). (Type your answer in interval notation. Use a comma to separate answers as needed.)

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Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

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Q: Explain, using the theorems, why the function Is continuous at every number In Its domaln. x- 9 Q(x)…

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Q: Determine the intervals on which the following function is continuous. x + 8 f(x) (x + 8)(x - 4)

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A: Given the function f(x)=(x2 + 4)/(x - 2) We need to use the definition of continuity to determine…

Q: Determine the intervals on which the following function is continuous. x - 7x+ 10 f(x) = %3! 2 x -4

A: f is discontinus a point  if limit is not exit at that point.

Q: Let f be defined in an open interval that contains a=3 and assume that all x,…

A: f be defined in an open interval that contains a=3 and assume that all x,2x+6≤f(x)≤x2-4x+15

Q: Determine the intervals on which the following function is continuous. x + 6 f(x) : (x + 6)(x + 8)…

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Q: Consider the following. -9x, f(x)=2 - 2x + 7, x > 6 Find the x-value at which f is not continuous.…

A: Givenf(x)=-9x ,   x≤6x2-2x+7  , x>6The function is continuous ifLHL=RHL =f(a)ie limx→a-…

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x + 7)/(x - 7) a…

A: Given, f(x)= x+7x-7 and point a= 7 To determine: f is continuous at a Definition of continuity :  A…

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Q: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

A: We have to check

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Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x - 5)/(x + 5) a…

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Q: Determine whether the following functions are continuous at a. Use the continuity checklist to…

A: Given: fx=2x2+3x+1x2+5x,a=-5

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Q: f(x) = x² + /7 – x, a = 4

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Q: Use the definition of continuity and the properties of limits to show that the function is…

A: We have to use the definition of continuity and the properties of limits to show that the function…

Q: Determine the​ interval(s) on which the following function is continuous. At which finite endpoints…

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Q: Determine if the following is continuous at the indicated value of x. If it is continuous determine…

A: Given that: f(x)=|3x-5|,    if -5≤x≤-14xx-1,        if  -1<x≤5     NOTE: As per our answering…

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A: f(x) = x4 − 81x is a polynomial function.

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Q: Determine the intervals on which the following function is continuous. X-8 f(X)= 2-64

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Q: 2. For the given function, f, determine if the function is discontinuous at a given point. State…

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A: The given function is: f(x)=x2-x-6x-3

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

A: Given function is

Q: Determine whether the statement is true or false. If f is continuous at 5 and f(5) = 3 and f(4) = 3,…

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Q: Use the definition of continuity to show that f is continuous at 2: f(x) = 3x2 – 2x + 1.

A: Definition of function continuity is: A function fx is said to be continuous at point x0 if and only…

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A: We will solve the problem

Q: Consider the following. -3x, f(x)= x² – 4x + 7, x > 2 Find the x-value at which f is not continuous.…

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Q: Explain why the function is discontinuous at 4 using definition of continuity. What type of…

A: Given f(x)=x2-x-12x-4 Explain why the function is discontinuous at 4 using definition of continuity.…

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Q: b) Discuss the continuity conditions of the function- f(x) which shown in figure at x= 0,x = 1,x= 2…

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Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4

Q: Determine whether the statement is true or false. If f is continuous at 5 and f(5) 5 and f(4) = 3,…

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Q: Identify the removable discontinuity and define the continuous extension of the function. x² + 7x –…

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Q: Determine the intervals on which the following function is continuous. x2 - 3x +2 f(x) = x2 - 1

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Q: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

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

A: Given f(x)=2x-3x-3

Q: Identify the removable discontinuity and define the continuous extension of the function. x² + 4x –…

A: We need to point where hole in function that point is removable continuity point

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.