Answer the following questions correctly in 2-3 sentences only (This is all about Continuity of a Function). 1. How to determine whether the function is continuous or not at a certain point? 2. How to determine whether the function is continuous or not on a closed interval? 3. How to illustrate the continuity or discontinuity of a function?

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: Assume whether the function graphed in the accompanying figure is continuous on [-1,3]. y = k(x) 2 3…

A: for being a contrinuous function this condition should be satisfiedlimx→a-f(x)=limx→a+f(x)=f(a)from…

Q: What three conditions must be met for a function ƒ to be continuous at the point (a, b)?

A: Continuity at points: The points of continuity are the points where a function exist and has some…

Q: 4 x if x 2 3 = x - 2 if 0 < x < 3 x-1 if x <0 %3D

A:

Q: 2. State whether each function in question 1 is continuous or not. If not, state where it is…

A: Definition of the continuous function is, Right hand side limit and Left hand side limit should be…

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

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Q: S(x + 4)² -2 < x x < -2 f(x)

A: fx=x+42    -2≤xx2              x&lt;-2 Since the given function is a polynomial function for all…

Q: Check the continuity of the following function at x = 1 (1+x f(x) = {x? 2-x if x<-1 if -1sx<1 if x…

A: A function is continuous at  x = a if the following condition is satisfied

Q: determine at which points, the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q is continuous.

A: Given To evaluate the points where the function f(x)=x2 if x∈Q if x and f(x)=-x2 if x∈R/Q    is…

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

A: Given, f(x)=x2-4x+3x-3   ifx≠32                  ifx=3;a=3 find the continuity of function at x=3 if…

Q: Is the following function continuous at x = 2? Explain why or why not. x2 +x – 6 - :x > 2 f(x) = x –…

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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: (x – 2)2 +1 if x 2

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

Q: { -2x + 3 x 1

A: We have given a piecewise define a function fx which definition change at x=1. The functions…

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: On what intervals are the following functions continuous? 8(x) = x³/4

A: To find: The interval of the function gx=x34 where the function is continuous. Concept: The function…

Q: Which of the following statements is false for a function f that can be differentiated at least…

A: We have to define which statement is wrong

Q: Determine whether the following function is continuous at a. f(x) = /x- 7; a = 1

A: Topic :- Continuity

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

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Q: At what points are the functions continuous?

A: The part of the function -x2 / 2 is always continuous. There is no point of discontinuity here. The…

Q: 1. Write the conditions a function has to meet in order to be continuous at point a. a) b)

A: A function f(x) has to meet these conditions in order to be continuous at any point a

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the function,fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: At what points is the following function continuous? 3 x - 125 x²2²-25 f(x) = 7.5, 4, X#5, x# -5 x =…

A: Given function:- fx=x3-125x2-25x≠5,x≠-57.5x=54x=-5 Condition for continuity at x=a…

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: Which of the following is a function that has a jump discontinuity at x = 2 and a removable…

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Q: Consider the function defined by f(x) = -(x + 1)² +5 if x 4 Graph the function. Is the function…

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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: 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: Answer the following True or False: If f(x) is defined and continuous on the open interval (a,b),…

A: The Extreme Value Theorem states that  If f(x) is defined and continuous on the closed interval [a,…

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

A: A function f(x) is continuous at a point c  if and only if the following three conditions are…

Q: Decide if the following function is continuous using limits. x1.

A: Given,          gx=2xx&lt;13x=13x2+3x&gt;1

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: f(x) = X-5 if xŹ 2 at x = 2 2x if x< 2

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Q: Decide if the following function is continuous using limits. x1. 2х g(x)= 3

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Q: Exercise 1.5. Determine whether the following functions are continuous at the indicated number. 1.…

A: For a function to be continuous at x = a, left hand limit = right hand limit = f(a)   Here we have…

Q: Determine whether the following function is continuous at a. Use the continuity checklist to justify…

A:

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

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

Q: Consider the piecewise function f(x) defined by 6 — 2х if x 4 х? — 16 For which x E R is f(x)…

A: Given function is fx=6-2x                            , if x≤4x-4x+4x-6x2-16    , if x&gt;4

Q: Part C: Check the continuity of the following function at x 1 1+x if x<-1 if -1sx<1 if x 21 f(x)…

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Q: f(x) to 2. 2.

A:

Q: For each of the following statements, write whether it is true or false. If true, provide a brief…

A: Given statements:   (a): Every continuous function defined on (-4, 0) must attain a maximum:…

Q: Prove that for functions f: R-R, the e-6 definition of continuity implies the open set definition.…

A: Open set definition of continuity: A function f ⁣ : R  → R   is said to be continuous if and only if…

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: Show that the following statement is false by drawing a graph that provides a counterexample: If f…

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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.