Use the three part definition of continuity to determine whether or not the given function is continuous at the given number. a. Explain your reasoning; be precise  if discontinuous, is it a removable discontinuity?

Q: Test the continuity of the following functions at given points? r2

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Q: Use the provided Cartesian plane to sketch the graph of the following functions. Then, determine the…

A: Given function is: fx=2x-10,x<22,x≥2 To sketch the graph of the given function in Cartesian plane…

Q: Use the definition of continuity to determine the value of the constant c for which the function f…

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Q: Use the graph to answer the question. Is f continuous at x = 0? 4- Yes No

A: The graph of the function fx is given by To evaluate: Whether the function is continuous at x=0 or…

Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

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Q: B. Determine the intervals wherein the function is continuous and the values of x wherein there is…

A: Check the graph of the function in problem 5 is continuous or not, Definition of continuous…

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: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x2 + 4)/(x - 2) a…

A: Given the function f(x)=(x2 + 4)/(x - 2) We need to use the definition of continuity to determine…

Q: Use the definition of continuity to determine whether f(x) = 2x + 5 at a = 1.

A: Given function is fx=2x+5.

Q: Use the definition of continuity to determine whether the shown is continuous at a = 2.

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Q: Determine the points where the given function is not defined and is therefore not continuous. For…

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

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Q: Use the definition of continuity to determine whether f is continuous at a.

A: Given :           f(x) =  1 - x      if x < 1             0           if x = 1            x2 - 1…

Q: Assume f(x) is continuous on (-infinity,infinity) Use the given information to sketch the graph of f

A: f' is positive implies f is increasing f' is negative implies f is decreasing f'' is positive…

Q: Use the definition of continuity to determine whether f is continuous at a. f(x) =(x - 5)/(x + 5) a…

A: If the function is continuous at x=a then it must satisfy the conditions of continuity.  The value…

Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

Q: Determine whether the following functions are continuous at a. Use the continuity checklist to…

A: Given: fx=2x2+3x+1x2+5x,a=-5

Q: (x – 2)2 +1 if x 2

A: We have to check continuity of function at x=0 and x=2

Q: f(x) = x² + /7 – x, a=4

A: We have sove limit and showing function

Q: f(x) = x² + /7 – x, a = 4

A: A function is said to be continuous on the interval [a, b] if it is continuous at each point in that…

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

A: We have to use the definition of continuity and the properties of limits to show that the function…

Q: f (x) 1 ; x = - 5 %3D | x+5

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

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Q: Use the definition of continuity to determine whether f is continuous at a.

A: Given: fx=x2-4x-2  if x≠25   if x=2 To Find:  To check whether the given function is continuous at…

Q: Use the definition of continuity to determine whether f is continuous at a.

A: To determine if a function is continous, it follows 3 conditions. The first condition is when the…

Q: 1. f(x) 2. f(x) = 3. f(x) x² - 4x X 2x x²-9 x² x-2 ; C = 0 -4 ; C = ; C = 2

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Determine where f(x) is continuous, algebraically. Enter the answer in interval notation.

A: Given data: The expression for the given function is f(x)=log18(10x+150)-7x. The given function is…

Q: Is f continuous at x = 2?

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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: Determine whether each of the given statements is true. Justify your response with an explanation or…

A: To Determine whether the given statement is True or False: If a function is not continuous at a…

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

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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: Find each x-value at which f is discontinuous and for each x-value, determine whether f is…

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Q: Define the term Continuity Conditions?

A: Given that: The term Continuity.

Q: Which of the following functions are continuous? Why do you think they are continuous? hix fix

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

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Q: Classify the statement as either true or false. If f is continuous at x= 2, then f(2) must exist,…

A: Given query is to find statement is true or false.

Q: Given the graph of f(x) shown below, which condition in the definition of continuity fails first at…

A: Continuous function=> left-hand limit and right-hand limit for a function x = a exists and  they…

Q: a) f(x) at x = 0 b) fx) 3x at x = -4 X-7

A: a) f(x)=6x at x=0b) f(x)=3xx-7 at x=-4

Q: 3. Use the definition of continuity and the properties of limits to show that the function is…

A: As per our guidelines we are supposed to answer only one question i.e. the question no (a). For the…

Q: Determine whether the statement is true or false. If f(x) is continuous at x = c, then so is f(x).…

A: Solution is given as below:

Q: Determine the continuity and, if discontinous, the type of discontinuity for the function…

A: Given query is to find function is continuous or not at x = -1.

Q: Consider the following figure. y f(x) whether the function is continuous or discontinuous at that…

A: Given query is to check the characteristics of function for x = -2.

Q: Determine

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Q: The function whose graph is given below is discontinuous at x = 1 because the third condition of…

A: We can answer the question as below

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.