Will a function that is differentiable on a given interval always be continuous on that interval? Explain. If this statement is not always true, provide an example of a function that proves it is false.

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

A: a rational function f(x)=p(x)q(x)   is discontinuous at point wheher q(x)=0

Q: Describe the properties of continuous  function?

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Q: List the  Properties of Continuous Functions?

A: given,       List the  Properties of Continuous Functions

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

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

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Q: x² -x-2 Is the function f(x) : Fcontinuous at x = 2? Why or why not? x-2

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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: 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: 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 continuous on an interval? Give examples to illustrate the…

A: In simple terms, if the graph of a function can be drawn without lifting the pen from the paper, we…

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 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: 4. Explain what it means for a function f to be continuous at a point x = c, with a sentence that…

A: Given: We have to explain about function f  to be continuous at a point x=c

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

A: Consider the given function: fx=x-1x-1 This can be written as a split function: fx=-1x<11x>1…

Q: Determine whether the function is continuous or discontinuous 5. f(x) =

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Q: say whether the function graphed is continuous on[-1, 3]. If not, where does it fail to be…

A: It is clear from the graph that  function y=g(x) is continuous in [-1,3) But at x=3, Therefore, g…

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

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Q: 1) If possible, give an example of where a function is differentiable at a point but not continuous…

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Q: In The given question, , determine whether the statement is true or false. If it is false, explain…

A: we have to tell whether the given statement is true or false. Statement : If a function is…

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

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Q: We informally describe a function f to be continuous at a if itsgraph contains no holes or breaks at…

A: Continuous function: A function fx is said to be continuous at point c if the following conditions…

Q: "If a function is continuous at some point then it must be differentiable at that point". Do you…

A: To show whether the given statement is true or false .

Q: Describe the intervals on which the function is continuous

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

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: What are the Limits of Continuous Functions?

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

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: Suppose f is a continuous function on [a,b] and suppose that f(a) 0 What can you say about the…

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

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

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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: 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: 2) If possible, give an example of where a function is continuous at a point but not differentiable…

A: Continuity of a function is the characteristic of a function by virtue of which, the graphical form…

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: 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: over what domain interval is f(x)=|x| increasing?

A: Consider the given function fx=x

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: 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: 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: 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: Adding two functions that are continuous everywhere yields a function that is continuous everywhere.…

A: given,         Adding two functions that are continuous everywhere yields a function that is…

Q: Can you conclude anything about the extreme values of a continu-ous function on an open interval? On…

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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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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.