What does it mean for a function to be left-continuous at a point?

Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

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Q: What does it mean for a function to be continuous on an interval?

A: A function is said to be continuous on the interval when the function is defined on every point of…

Q: Is every continuous function differentiable? Is every differentiable function continuous? Explain.

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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: What can be said about algebraic combinations and compositions of continuous functions?

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Q: 1. How to determine whether the function is continuous or not at a certain point?

A: As per our guideline we are supposed to be answer only one question please repost the other question…

Q: Explain how to find the extrema of a continuous function on a closed interval [a, b].

A: First, you have to find f'(x) Then solve f ' (x)=0 to find the critical points.  Take the critical…

Q: Describe the properties of continuous  function?

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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: 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: Determine whether the statement is true or false. If it is false, explain why or give an example…

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

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Q: What does it mean if a function f is increasing on an interval?

A: Let the given function be y = f(x) And the interval be I.

Q: What does it mean for a function to be right-continuous at a point?Left-continuous? How are…

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Q: Will a function that is differentiable on a given interval always be continuous on that interval?…

A: Given the statement that " Will a function that is differentiable on a given interval always be…

Q: What does it mean for a function to be right-continuous at a point?

A: A function f is right continuous at a point c if it is defined on an interval [c, d] lying to the…

Q: Determine the intervals on which the function is continuous. %3!

A: To find: The interval in which the function fx=12-x is continuous. Concept used: The domain of the…

Q: How does  a function behave near a particular point at which we cannotdirectly evaluate the…

A: To understand the concept we will consider an example

Q: b) State what it means for a function to be continuous at a point x = a.

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Q: Explain the difference between the Discrete and Continuous Variables.

A: Discrete Variables are the variables whose values are obtained by counting since these variables…

Q: function is continuous.

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Q: = Find a continuous function

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Q: Which of the following functions are continuous? Why do you think they are continuous?

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Q: Explain why functions with corners are not differentiable even though they are continuous.

A: A differentiable function of one real variable is a function whose derivative exists at each point…

Q: Determine whether the statement is true or false. If it is false, explain why or give an example…

A: The given statement is false.Because it is not necessary that if a function is continuous then it…

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: What are the Limits of Continuous Functions?

A: Given, What are the limits of continuous functions?

Q: How do you find the absolute maximum and minimum values of a function that is continuous on a closed…

A: Consider the provided statement to find the dimensions that provided maximum area and has perimeter…

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

A: Given: Condition of whether a function is continuous at a number

Q: At what points are the functions continuous?

A: The part of the function -x2 / 2 is always continuous. There is no point of discontinuity here. The…

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

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

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

Q: Write the Intermediate Value Theorem for Continuous function?

A: Intermediate value theorem: Statement: The intermediate value theorem states that, If f is a…

Q: Describe the process of linearization of a function f(x) at a point x = a, and explain how it can be…

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Q: V16-x2 f(x) = at (-3,-1) x+1

A: Given function is fx=16-x2x+1 The interval is -3,-1 We know that function is continuous in any…

Q: Give the three conditions that must be satisfied by a function to be continuous at a point.

A: We have to write  the three conditions that must be satisfied by a function to be continuous at a…

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

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

Q: Is it true that a continuous function that is never zero on an interval never changes sign on that…

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Q: V16-x3 f(x) = at (-3,-1) x+1

A: Here given function  fx=16-x3x+1 Draw the graph of the given function as

Q: Is the function continuous or discontinuous? If discontinuous, what condition is not satisfied?

A: Given:

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: Is the function continuous or not? If not, what condition is not satisfied? Present solution

A: A function fx is said to be continuous at a point at x=c if 1. fc is defined and exists 2.…

Q: Which of the following does not represent a function that is continuous everywhere?

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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: Identify three cases for a function NOT to be differentiable at a. Explain why each case fails the…

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Q: What is the extrema of a function?

A: what is the extrema of a function

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.