Need help with this question: find the limit of the function shown in the image below.

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ishpiro | College Teacher | (Level 1) Educator

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The fourth choice is the correct answer: the limit does not exist.

Consider the given function f(x) as x approaches 2.

If x is approaches 2 from the right, that is, x remains greater than 2, then the function will approach 22.20, the value of f(x) on the interval (2, 3], given by the third branch. This can be written as

`lim_(x->2^+) f(x) = 22.20` , or right-sided limit at 2 is 22.20.

If x approaches 2 from the left, that is, x remains less than 2, then the function will approach 18.30, the value of f(x) on the interval (1, 2], given by the second branch. This can be written as

`lim_(x->2^-)f(x) = 18.30` , or left-sided limit at 2 is 18.30.

When the right-sided and left-sided limits are not equal to each other at a given point, the limit does not exist at that point.

Note that it does not matter that f(x) is defined at 2 as f(2) = 18.30. The limit is determined by the value that the function approaches when x approaches 2, independently of what the value of f(x) is at 2.

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