Explain how to determine whether a function is continuous at a number.

Q: Carefully sketch the graph of a continuous function f which satisfies the following properties:

A: Given, Sign of f'x-f'x<0 on an interval -∞,-2. f'x>0 on an interval -2,0. f'x<0 on an…

Q: Describe a function with an oscillating discontinuity at 0.

A: We need to describe a function which has an oscillating discontinuity at x=0.

Q: Find the values that make the piecewise function continuous:

A:

Q: What does it mean for a function to be differentiable on an open interval? On a closed interval?

A: If a function f is differentiable on an open interval (a,b) then it means that the function is…

Q: Describe the intervals on which the function is continuous. f(x) = −3x2 + 7

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Q: Explain how you might differentiate a piecewise function like |x| When it's differentiable, for…

A: We can use the concept of calculus and function in order to solve the given question.

Q: Give an example of continuous function?

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Q: What can be said about the extreme values of a function that is continuous on a closed interval?

A: To Determine: What can be said about the extreme values of a function that iscontinuous on a closed…

Q: Determine the interval on which the function is increasing and the interval on which the function is…

A: For the function with above graph, we need to determine the interval on which it is increasing and…

Q: Please illustrate the difference between a function being continuous and differentiable by…

A: We have to  illustrate the difference between a function being continuous and differentiable…

Q: identify whether the following functions are continuous or not.

A: We are given with multiple question our guideline is solve first question kindly repost remaining…

Q: Explain why a function with a removable discontinuity is not differentiable at that discontinuity

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Q: It is impossible for an even function to be increasing on its entire domain.Determine whether the…

A: Function is even if f-x=fx for all x∈domain If  x∈domain this implies that -x∈domain Suppose…

Q: Give an example of Piecewise-Defined Functions?

A: By a piecewise defined function, a function of the form

Q: Identify all intervals over which the function is increasing.

A: NOTE: Refresh your page if you can't see any equations. . as we can see from the graph, the…

Q: Graph the function f. Then determine whether or not the function is continuous.

A: We need to draw the  graph of given function and we need also need to check whether f(x) is…

Q: How many x-intercepts can a function defined on an interval have if it is increasing on that…

A: It is asked to explain the number of x-intercepts can a function defined on an interval have if it…

Q: Describe the intervals on which the function is continuous.

A: Discuss the interval on which the function is continuous

Q: Determine whether the function is continuous at the given point. Show your solution.

A: This question is taken from the continuity and discontinuity in which we have to check whether a…

Q: Write an equation that expresses the fact that a function f is  continuous at the number 4.

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Q: Describe the intervals on which the function is continuous.

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Q: Write the Properties of Continuous Functions?

A: Given functions is continuous function.

Q: Describe the intervals on which the function is continuous. f(x)= 4x2+7x-2 / x+2

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Q: function is continuous.

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Q: Describe the intervals on which the function is continuous

A: fx=-3x2+7 It is a polynomial function of degree 2.

Q: Identify the open intervals where the function is changing as requested. Decreasing

A: We have to find the interval where the function is decreasing.

Q: How can looking at the graph of a function help you tell where the function is continuous?

A: For the graph of function to be continuous, it needs to be smooth without any holes, jumps, or…

Q: Determine whether  the following statement is true or false, and explain why. If ƒ″(x) > 0 on an…

A: If the second derivative of a function f(x) is defined on an interval (a,b) and f ''(x) > 0 on…

Q: When is a function of two (three) independent variables continuous at a point in its domain? Give…

A: When is a function of two (three) independent variables continuousat a point in its domain? Give…

Q: When is a function of two (three) independent variables continu-ous at a point in its domain? Give…

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Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

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Q: Explain why the function is discontinuous at a =2 by checking all three conditions for continuity.…

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Q: The boxes that are checked correspond to functions that are: Increasing Decreasing

A: We need to provide boxes that are checked when a funtion is increaing and decrasing.

Q: Describe how to tell when a function is discontinuous at thereal number x = a.

A: There are three conditions that need to be satisfied by a function f(x) in order to be continuous at…

Q: Is this function Discrete, continuous, piecewise, or linear?

A: as we can see here graph does have scattered points so the given function is not Discrete. now, as…

Q: What does it mean for a function to be continuous on an interval?Give examples to illustrate the…

A: For open intervalIf f:(a, b)→ℝ is defined on an open interval, then f is continuous on (a, b) if and…

Q: Estimate the intervals where the function is increasing or decreasing.

A: Given: The graph of the function is, To find: Where the function is increasing or decreasing.

Q: What is the sign-preserving property of continuous functions?

A: What is the sign-preserving property of continuous functions?

Q: Describe the interval(s) on which the function is continuous. (Enter your answer using interval…

A: The given function is f(x) =xx2 + x + 2. The main objective is to find the interval in which fx is…

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: Determine the set of points at which the function is continuous

A: f (x, y, z) = sin-1 (x2 + y2 + z2) = t (Let's say)Hence, sin t = (x2 + y2 + z2)

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

A: Continuous function: A function f(x) is continuous over an interval [a,b] if the function has no…

Q: Discuss the continuity of the function

A: In the question we have to find the continuity of the function.

Q: Describe the intervals on which the function is continuous.                           f(x) = (4x2 +…

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Q: DISCUSS THE CONTINUITY OF THE FUNCTION ON THE CLOSED INTERVAL

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Q: State the intervals on which the function f is continuous

A: A function is said to be in an interval if it's graph runs continuously without any break it that…

Q: Not every differentiable function is continuous

A: If a function is said to be differentiable at its domain then it must be continuous in its domain.…

Q: examine the continuity of the function

A: Given function is not defined at x=0

Q: why the function is continuous at every number in its domain. State the domain.

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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.