When is a function of two (three) independent variables continu-ous at a point in its domain? Give examples of functions that are continuous at some points but not others.

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

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Q: Determine whether a function is continuous at a given number. If it is discontinuous, identify which…

A: Given: fx=x2-9  , x<35 ,           x=39-x2,    x>3

Q: Determine whether function is continuous and/or differentiable at x = 1. f (x) = 1/x

A: Consider the given function fx=1x

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: Either a function is not differentiable at a point or it is continuous at that point. O True False

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

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Q: Is it possible for a function to satisfy f(x) > 0, f′(x) > 0, andf ″(x) < 0 on an interval?…

A: We want function that is: 1. positive on interval I since fx>0   2. increasing on interval I…

Q: What is the domain of the secant function?

A: Secant function , Sec xWe know        Sec x=1cos xTo find domain Put cos x=0

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: 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: The function is discontinuous at x= -4. At this point, is f continuous from the right, left, or…

A: A function f is said to be right continuous at a point a if it is defined on an interval and if…

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: 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: 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 or discontinuous 5. f(x) =

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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: 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: List the points in the graph at which the function is not differentiable.

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Q: Given the graph below, what can you say about the function at (-1,1)? Not Continuous Continuous

A: The graph of a function is said to be continuous if the value of the function exists for all values…

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

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

Q: Find continuous functions

A: Given,        fn:0, 1→[0, ∞)

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

A: Derivative is a slope, defined by a limit.   In order for a derivative to exist, it needs to be…

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: 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: find domain of Function composition f(x)=,

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

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

Q: The graph of the function f'(x) of a continuous function f is shown. On what intervals is f concave…

A: It is given that,the graph of the function f'(x) of a continuous function f.  We have to find…

Q: Explain Why functions with cusps are not differentiable even though they are continuous.

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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: 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: sketch the graph of a function that is continuous everywhere except at x=3, and is continuous from…

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

A: Given:

Q: If f is even and differentiable function, the x = 0 is a critcal number of f. True or False

A: Known fact: For even differentiable function, 0 is a critical number.

Q: Is the function continuous at the point being approached?

A: The given function is limy→1sec(y*sec2y-tan2y-1)   We have to check whether this function is…

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: Is the function continuous from X = -5 to x = 0? This function is made up of four (4) linear…

A: 1. True, the function is continous from x=-5 to x=0 as there is no break in the       graph between…

Q: In calculus was claimed  that increasing (or decreasing ) functions  defined on a single interval is…

A: Consider a one - to - one function in an fixed interval.  For the function f(x), in the interval 0…

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.