Give an example of continuous function?

Q: Is the product of two increasing functions always increasing? Explain.

A: Given: The statement is “the product of two increasing functions is always increasing”. Here, the…

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

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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: How to form a piecewise function by using linear function?

A: The piecewise function can be formed using linear functions as shown below.

Q: What events in life can you compare to continuous functions?

A: A function is a continuous function if the graph of the function is not breaking at any point in its…

Q: Describe the properties of continuous  function?

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

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Q: Give a geometrical interpretation of the function In x

A: To give: Geometric interpretation of the function ln x=∫1xdtt. Concept used: The area under the…

Q: List the  Properties of Continuous Functions?

A: given,       List the  Properties of Continuous Functions

Q: What are the limits of function values?

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

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Q: Find a function £

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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: 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: Can a function be both even and odd? Explain.

A: To check whether a function can be both even and odd.

Q: Give an example to explore numerically how a function behaves near a particular point at which we…

A: Solution: Consider y = f(x) = 1/x is the function Since at x = 0, this function is going to be…

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

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

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Q: Define Increasing and decreasing function?

A: According to the question, we have to define the increasing and decresing function. To check the…

Q: Write the Properties of Continuous Functions?

A: Given functions is continuous function.

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: 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: Define the Limits of Function Values?

A: Limits of Function Values: Let f be a function such that limx→afx=L  means for every  ε>0 there…

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: Describe what is the relationship between differentiability and continuity of a function.

A: To explain: The relationship between differentiability and continuity of a function. Explanation:…

Q: What do all members of the family of linear functions f(x)=  c- xhave in common? Sketch several…

A: Given :           fx=c-x

Q: This is a function. Truc

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Q: Determine whether the function shown is continuous over the interval (-5, 5). No Yes

A: We have to determine the given graph is continuous or not in the interval (-5,5).

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

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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: Give an example of a discontinuity function?

A: If f(x) is not continuous at x=a , then f(x) is said to be discontinuous at x=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: Give an algebraic example of a function that will have a jump discontinuity.

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Q: Briefly explain what the Mean Value Theorem tells us. Why do we require that f be a continuous…

A: Explanation given below...

Q: define convolution of two functions?

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Q: Discuss the continuity of the function

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

Q: Vx+50-5 f(x) = at (-5,-1) х-20

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

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Q: examine the continuity of the function

A: Given function is not defined at x=0

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: Are all odd functions always decreasing? Explain

A: DEFINITION OF ODD-FUNCTION: An odd function f (X) is a function such that for every value of X ,…

Q: Give Definition of Even Function ?

A: A function fx is said to be the even function if it satisfies the condition as, f-x=fx, for any…

Q: 3 Can a function be always concave down and never cross zero? Can it be always concave down and…

A: The 1st answer is Yes and 2nd is No.

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.