Which of the Following Function Has a Removable Discontinuity

116326092012 a We need to check whether the function has a removable discontinuity at or not. By redefining the function we get.

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If an answer does not exist enter DNE a fx 1 a 1 O The discontinuity is removable.

. Suppose f x is. See also why are snails important to the environment. B f x x3 x2 56x x 8 a 8 g x.

The given function is not continuous at x -2. Fx3 x9 x at x9. Fx can be redefined as.

Agrees with f for x a and is continuous at a. Fx x 2 - 2x - 8x 2 x - 4 x - 2x - 2 fx x - 4 f-2 -2 - 4 -6 Hence the given function has removable discontinuity at x 2. Observe that the function f is not defined at x1 and hence function is not continuous at x1.

If the function have a removable discontinuity redefine the function so as to remove the discontinuity f x 4 x - e x 6 x - 1 for x 0 log 2 3 for x0 Advertisement Remove all ads Solution f 0 log 2 3 Given. Which of the following functions has a removable discontinuity at a. F x.

Which of the following functions f has have a removable discontinuity at the indicated pointA. Fx e5sinx - e2x5tanx - 3x x. Fx has a removable discontinuity at x 0.

O The discontinuity is not removable. If the discontinuity is removable find a function g that. X 1 l im 2 2 1 x 1 1 and x 1 l im 2 2 1 x 1 0.

Lim x 4 f x does not exists. G x begin cases f x text if xneq 2 6 text if x 2. Fxx2 2 x 8x2 at x 2B.

G x b f x x3 - x2 - 20x a 5 X-5 The. From the given function we see that the given function is not defined at because division by zero is not possible. Fxx 7x 7 at x7C.

If an answer does not exist enter DNE a f x x4 1 x 1 a 1 g x. The above function tells us that the graph generally follows the function f xx2-1 except for at the point x4. The function eqbffx eq has a removable discontinuity at eqbfx0 eq and a nonremovable discontinuity at eqbfx-2 eq.

In order to redefine the function we have to simplify fx. Find step-by-step Calculus solutions and your answer to the following textbook question. Consider a function y fx and assume that it has removable discontinuity at a point a fa.

A Neither f x nor g x has a removable discontinuity because they both have vertical asymptotes. This question has multiple correct options. Answered 2021-11-18 Author has 10 answers.

If the discontinuity is removable find a function g that agrees with f for x a and is continuous at a. Discuss the continuity of the following functions. If the discontinuity is removable then we need to find a function g that agrees with f for and is continuous on.

Fxx364x4 at x 4D. F x exists and this limit is finite and there are two types of removable discontinuities which are the function is undefined at x a and the value of the function at x a does not match the limit and when a function has a removable discontinuity it can be defined to make it continuous function. A Explain why f has a removable discontinuity at x 4.

If an answer does not exist enter DNE a f x a 1 X-1 The discontinuity is removable. O g x has a removable discontinuity at x 5 where there is a vertical asymptote. Which of the following functions f hashave a removable discontinuity at the indicated point.

X 1 l im x 2 x x 1 2 x 2 2 1 Rationalizing fx has removable discontinuity at x 1. If the discontinuity is removable find a function g that agrees with f for x a and is continuous at a. Hence the limit does not exist.

O F x has a removable discontinuity because although the graph appears to be continuous at x -4 the function is undefined for the domain value x -4. Find step-by-step Calculus solutions and your answer to the following textbook question. The removable discontinuity is a type of discontinuity of functions that occurs at a point where the graph of a function has a hole in itThis point does not fit into the graph and hence there is a hole or removable discontinuity at this point.

If the discontinuity is removable find a function that agrees with f for x is not equal to 0 and is continuous at a. This discontinuity can be removed by redefining f0 32. End cases g x f x 6 if x 2 if x 2.

When we graph it we will need to draw a little open circle at the point on the graph and mark that it equals 2 at that point. If the discontinuity is removable find a function g that agrees with ffor x a and is continuous at a. Limits and Continuity Playlist.

Now we need to simplify the given. Some functions such as polynomial functions are continuous everywhere. A function has a removable discontinuity if it can be redefined at its discontinuous point to make it continuous.

Consider the following function. A removable discontinuity can be created by defining a blip in the graph like this. Which of the following functions f has a removable discontinuity at a.

G x f x if x 2 6 if x 2. Other functions such as logarithmic functions are continuous on their domain. Since the limit exists at x2 and therefore x2 is a removable discontinuity.

Gx X b fx x - x2 56 a 8 x -. 1 lim x 0 - f x lim x 0 - 4 x - e x 6 x - 1. Which of the following functions f has a removable discontinuity at a.

Example 1 - Piecewise Function with a Removable Discontinuity Consider the function f x left begin array rc 6x-2 x 2 8x x 2 end arrayright. Fx has removable discontinuity at x 1 c. Fx x4-1x-1 a 1.

Select all that apply a. F x x 4 1 x 1. C f x sin x a π Recall that h x means the largest integer that is less than or equal to h x g x.

We want to see whether it has a removable discontinuity. The discontinuity is not removable. F 4 and lim x 4 f x exist but are not equal.

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