Determine analytically using the three part definition of continuity whether the given function is continuous at 5. Explain your reasoning. If discontinuous is the discontinuity removable?

Q: Determine the domain of the function and prove that it is continuous on its domain using the Laws of…

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Q: Is the function f graphed below is continuous at = -4? Choose the appropriate reason that justifies…

A: topic - continuity and limits f is not continuous at x =-4 reason = left hand limit is not equal to…

Q: sify whether f(x) is continuous or discontinuous at the point/s. If disco x – 2 x <-1 f(x) = { x² +…

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Q: Determine the discontinuities of the following functions and state why the function fails to be…

A: f(x)=x3+x2-17x+15x2+2x-15function is undefine when x2+2x-15 is become 0Let…

Q: To Let f(x) = 1 Using the definition of continuity, show that f is cc

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Q: Find f(2) Is f continuous at x = 2? Explain your answer.

A: Given function

Q: How is a function’s differentiability at a point related to its continuity there, if at all?

A: If a function is differentiable at any point there it has to be continuous. For example: y= x^2 has…

Q: Explain, using the theorems, why the function Is continuous at every number In Its domaln. x- 9 Q(x)…

A: Given: Q(x)=x-93x3-9 To find: The domain and Why the function is continuous at every number in its…

Q: Discuss the continuity of f(x) = (that is, determine if the function is continuous or discontinuous…

A: To Discuss: The discontinuity of function  fx=x2-1x-1. Given: The given function is fx=x2-1x-1.…

Q: Give an example of a function ƒ(x) that is continuous for all values of x except x = 2, where it has…

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Q: Decide if the following function is continuous using limits. 2x,x0

A: We use left hand limit, right hand limit and function value at 0.

Q: For function f, how would you remove the discontinuity? In other words, how would you define f(5) in…

A: For continuity limit of function at a point should be equal to functional value at that point.

Q: For each given x-value, use the figure to determine whether the function is continuous or…

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Q: Use the definition of continuity and the properties of limits to show that the function is…

A: Given:               h(t) = 2t-3t21+t3,  a = 1 Definition of continuity: A real-valued function f(x)…

Q: 2x - 5x – 3 7. f(x) = if x # 3 x- 3 ,a = 3 6 if x = 3

A: Since you have asked multiple question,As per our policy we will solve the first question for you.…

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: 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: 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: Use the definition of continuity and the properties of limits to show that the function is…

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Q: Next qu Classify the statement as either true or false. If lim F(x) exists, then F could be…

A: We have to find out the continuous property

Q: f(x) = (x + 2x³)“, , a = -1 %3D

A: Limits Limit of the function at point a exists if and only if  left hand limit and right hand limit…

Q: - 2x+3, for x 1 4. .a = 1

A:

Q: Use the definition of continuity and the properties of limits to show that the function is…

A: Given,           ht=2t-3t21+t3 , a=1

Q: Suppose that (picture) If f is  continuous for all real numbers, then c is equal to:

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Q: fx +1 1 if x = 1 5. f(x) = ,a = 1

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Q: x + 1, for x > 2 f(x) = 2 3-x. for x < 2 6. ,a = 2

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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: Determine if the given function is continuous at a given value of x.

A: This question is related to limits and continuity, we will solve it using given information.

Q: Use the definition of continuity, along with the One- sided continuity theorem, to determine whether…

A: We first find left and right hand limit at x=4If left hand limit=f(4)=right hand limit, then the…

Q: 11. ((x) – (x + 2r'), a--1

A: To find the limit.

Q: Recall from calculus, if a function is differentiable at a point c, then it is continuous at c, but…

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Q: Use the definition of continuity to determine where f(x) is continuous. If it's discontinuous point,…

A: We will solve the problem

Q: Use the three part definition of continuity to determine whether or not the given function is…

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Q: Explain why the function is discontinuous at a =2 by checking all three conditions for continuity.…

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Q: Sketch the graph of a function f that is continuous except for the stated discontinuity.…

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Q: (-2x + 3, for x<1 S(x) =. x', for xz1 2, ,a=1

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Q: Explain why the function is discontinuous at 4 using definition of continuity. What type of…

A: Given f(x)=x2-x-12x-4 Explain why the function is discontinuous at 4 using definition of continuity.…

Q: Define the term Continuity Conditions?

A: Given that: The term Continuity.

Q: Suppose f" is continuous on (-o, 0). (a) If f'(2) = 0 and f"(2) = -2, what can you say about f? (b)…

A: Application of derivative problem

Q: determine whether or not the function is continuous at the indicatedpoint. If not, determine whether…

A: We have given a function f(x).

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

A: Given:

Q: Find the x-values (if any) at which f is not continuous. Which of the discontinuities are removable?…

A:

Q: Describe the type of discontinuity at x = -1, explain your answer. Use the definition of continuity…

A: a. Type of Discontinuity: Removable Discontinuity

Q: 2x - 5x – 3 ifx # 3 (6ifx= 3 7. f(x) = x-3 , a = 3

A:

Q: Use the three part definition of continuity to determine whether or not the given function is…

A: Here we will use three part definition of continuity of function

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: Determine

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Q: (- 2x +3, for x 1 0, for x 1 %3D ,a = 1 3.

A: Authoring guidelines:…

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.