How do you find the limit of (|x-7|)/(x-7) as x approaches 7?

inhaltynuaddyh4b

inhaltynuaddyh4b

Answered question

2023-02-14

How to find the limit of | x - 7 | x - 7 as x approaches 7?

Answer & Explanation

nebnikwjq

nebnikwjq

Beginner2023-02-15Added 6 answers

The left and right limits disagree, so there is no limit as x 7
Explanation:
If x > 7 then | x - 7 | x - 7 = x - 7 x - 7 = 1
If x < 7 then | x - 7 | x - 7 = - ( x - 7 ) x - 7 = - 1
Thus:
lim x 7 + | x - 7 | x - 7 = 1
lim x 7 - | x - 7 | x - 7 = - 1
Since the right and left limits are unequal, there is no two sided limit at x = 7 .
graph{abs(x-7)/(x-7) [4.24, 9.79, -1.266, 1.508]}

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