What is the relationship between functions whose limits can be obtained by direct substitution and the definition of continuous function?

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

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Q: What are the basic properties of limits of functions of two independent variables?

A: What are the basic properties of limits of functions of two independent variables?

Q: How can we find the Absolute Extrema of a Continuous Function ƒ on a FiniteClosed Interval?

A: How can we find the Absolute Extrema of a Continuous Function ƒ on a Finite Closed Interval?

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

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Q: I do not understand how to find limits in a function... at all...

A: Plug the given number x which is approaching in the function.

Q: What is the Limit of constant function?

A: The limit of a constant function is constant.   For example: Consider the constant function: In…

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: 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: 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: 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 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: How do we identify if the limit of a function exists or not?

A: Limit, depends on the possibility of closeness, utilized principally to allocate qualities to…

Q: How can we solve or find the limit of a function using or given the graph?

A: Limit of a function at a given value can be found by using the graph.

Q: Discuss the continuity of the function on the closed interval.

A: to find: limx→-1x3+3

Q: Define the term Limit of a Function?

A: The limit of function can be stated as the limit of a function is the appraoched value of the…

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

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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: Differentiate the power function f(x)=x4 using the limit definition.

A: Given: fx=x4

Q: What is an Informal description of the Limit of a Function?

A: Informal description of the Limit of a Function:

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 the points at which the function f (x) is continuous and the points at which f is…

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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: fully continuous for all x E R by use of the product rule differentiate the function f{x} = x3e-4x

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Q: Show that the function f(x)=x|x| is continuous and differentiable at x = 0

A: To show that f(x)=xx is continuous at x=0 To show that limx→0xx=00=0 use piecewise definition for…

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: Why is it important to know the concept of limits and limit of a function? Explain thoroughly

A: Concept of limit is very useful as this gives us the intense idea of approaching towards infinity.…

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 are the variety of important types of functions frequently encountered in calculus?

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Q: limit of a function f(x) as x approaches c is always equal to f(x). True or false

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Q: I realized that continuity of function is _______________________________________ I can apply what…

A: A function is continuous at a point if the three following conditions are met: 1) f (a) is defined.…

Q: What do you think why certain limit of a function does not exist? What are the conditions to…

A: we know that limit is exist when we approach to at that certain point on graph, from left and right…

Q: How can the definition be used to verify limit statements for specific functions?

A: Let fx be the function of x. If for every positive number ∈ , however, small it may be , there…

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: Estimate the one-sided limits for the function below.  f(x)=(11−x)/(x−8)^2

A: Given:

Q: Does the limit of a function depend on how the function is defined at the point being approached?

A: We know that, For the limit of a function to exist at a point, the functional values must approach a…

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: What do you mean by limit of a function that can be transformed using rationalization

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

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Q: Show that a function cannot have two different limits at the same point. That is, if limx-->c…

A: Let f(x) be a function which is defined everywhere in an interval except x=a, then , If for all ,…

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

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

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

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