How do you find the limit as x approaches 2 of the piecewise function f(x)= {(4-x^2, if, x le 2),(x-1, if, x>2):} ?

Vanduohp

Vanduohp

Answered question

2023-02-17

How to find the limit as x approaches 2 of the piecewise function f ( x ) = { 4 - x 2 if x 2 x - 1 if x > 2 ?

Answer & Explanation

Joaquin Edwards

Joaquin Edwards

Beginner2023-02-18Added 6 answers

Since the left-hand limit and the right-hand limit at x = 2 do not match, the limit lim x 2 f ( x ) does not exist.
Let's look for the limit on the left.
lim x 2 - f ( x ) = lim x 2 - ( 4 - x 2 ) = 4 - ( 2 ) 2 = 0
Let's look for the right-hand limit.
lim x 2 + f ( x ) = lim x 2 + ( x - 1 ) = ( 2 ) - 1 = 1
Since the above one-sided limits at x = 2 do not match, the limit at x = 2 does not exist.

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