Determine if the limit exists and if there is continuity or discontinuity for the attached file of functions

Q: Evaluate the limit and the function.

A: Here we take N tends to infinity for finding the limit function

Q: Evaluate the limit if f(x) = 8x on [0,5].

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Q: Assign values of x using the three special functions, and to get the values of y using scientific…

A: 1. f(t)=sintt   t f(t) 1 0.84147 0.5 0.95885 0.1 0.99833 0.01 0.99998 0.001 0.99999…

Q: Use formal definitions to prove the limit statements

A: Given: Function  To Prove:  Formal Definition Of Limit:

Q: A function is said to have a horizontal asymptote if either the limit at infinity exists of the…

A: limx→∞ x2+8x3-11x=limx→∞ 1xx2+8x1x(3-11x)=limx→∞ x2+8xx23x-11

Q: Create a table of values for the function and use the result to explain why the limit does not…

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Q: DRAW THE GRAPH OF A FUNCTION WHERE limr-a f(x) DOES NOT EXIST FOR SOME INTEGER a. EXPLAIN WHY THE…

A: To draw a graph of function where limx→afx does not exist for some integer a

Q: Decide whether the limits exist. If a limit exists, find its value.

A: Evaluate: limx→-∞ 38+3x-6x2

Q: use the formal definition of limit to prove that the function has a continuous extension to the…

A: Given function is fx=x2-1x+1 and point is x=-1

Q: Find the following limits if they exist. lim

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Q: use the formal definition of limit to prove thatthe function has a continuous extension to the given…

A: The given function is gx=x2-2x-32x-6. Note that at x=3, the above function is not defined. Thus,…

Q: Create a table of values for the function and use the result to explain why the limit does not…

A: Given: Function  Consider few values less than 0 and few values greater than 0 Then evaluate…

Q: Suppose that f has a one-sided limit at each point of fa, b. Prove that f is bounde

A: In mathematics, a function f defined on some set X with real or complex values is called bounded if…

Q: Evaluate the limit using continuity.

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Q: Find the limit of the following functions:

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Q: If f is an odd function and if lim f(x) exists Prove that this limit must be zero.

A: if limit is exist then right hand limit and left hand limit must be equal

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: evaluate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or…

A: We get 0 in the denominator , so the limit does not exist.

Q: Determine the limit graphically, if it exists. lim f(x)= x +1+ f(x) it + 1 -5 -4/-3 -2 -1 -1- 4 5 x…

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Q: Determine whether each of the following statements is true or false, and explain why.If the limit of…

A: If the limit of a function exists at a point, then the function is continuous there.

Q: Find the limit, if it exists, or show that the limit does not exist.

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Q: Create a table of values for the function and use the result to explain why the limit does not…

A: To create a table of values of x for the function limx→02x3, take the values of x nearer to 0, that…

Q: Determine whether each of the following statements is true or false, and explain why. If the limit…

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Q: Sketch the graph of a function that approaches a limit as x →∞but does not approach a limit (either…

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Q: Give the intervals where the limit exists for this function:

A: The graph shown in the question is as - Above graph is the graph of the function f(x)=cos(πx) Since…

Q: Give an example of functions f and g and a point x = a such that the limit of f as x approaches a…

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Q: Evaluate the limit if f(x) = 6x on [0, 3]. (Give your answer as a whole or exact number.)

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Q: What is the Limit of identity function?

A: we have to tell what is the limit of an identity function.

Q: EVALUATE THE LIMIT OF THE GIVEN FUNCTIONS

A: Given, To find limx→∞ x42x-12

Q: Calculate the value of the limit, if it exists, or show that it does not exist.

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Q: Sketch a graph of each of the following functions to determine the limit. If a limit fails to exist,…

A: Given that: limx→π4csc x

Q: Prove the limit as x approaches -2 of f(x)= 10x + 19 is -1 using the definition of a limit of a…

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Q: 2. f (x) 3 - 2x² if xくQ こ 2 メ if x 2 2

A: f(x)= x3-2x2 ; x<22-x ; x≥2       a=2 , if f is differentiable , then f'(2) should be finiteusing…

Q: Determine the following limits or state that they do not exist.

A: Given,

Q: Determine whether the limit exists. If so, find its value.

A: Let the given limit be y - y = lim(x,y)→(0,0)x4-64y4x2+8y2y = lim(x,y)→(0,0) x22-8y22x2+8y2y =…

Q: evaluate the limit if it exists. If not, determine whether the one-sided limits exist (finite or…

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Q: A function is defined as , (1/x-2) - (c/x2-2x). Calculate the limit of the function as it approaches…

A: Consider the given function…

Q: Find the limit of the following function, if the limit does not exist, show why

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Q: Determine the following limit in simplest form. If the limit is infinite, state that the limit does…

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Q: Define the following Symmetry Point of Intersection Limit Continuity…

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Q: Use the definition of the limit of a function to prove that if lim,a f(x) = L then lim,a+ f(x) =L…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: use the formal definition of limit to prove that the function has a continuous extension to the…

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Q: Decide whether the limit exists. If it exists, find its value. fx) 3+ 2+ -2 -1 3 X -1+ -2- 1) lim…

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Q: In Figure 17, determine the one-sided limits at the points of discontinuity. Which discontinuity is…

A: From the graph we can see that y→∞ as x→0 from the left side and y→2 as x→0 from the right side.…

Q: Use the graph to determine the limit and discuss the continuity of the function.

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Q: Let f(x) = – 3x + 4. According to the definition, f'(x) = lim |(enter the limit in reduced form)…

A: The given function,  f(x)=-3x+4

Q: evaluate the limit if it exists. If not, determine whether the one-sided limits exist (finite or…

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Q: ズッバty) Dim tan (x+9

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Q: Give an example of the limit of a function at a boundary point of its domain?

A: (A) Domain Let f be domain of function and f(x,y) be defined by f(x,y)=(x2y22/(x2y2+(x−y)2) The…