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Question
In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?
`lim_(x -> 5) |x - 5|/(x - 5)`
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Solution
`lim_(x -> 5) |x - 5|/(x - 5)`
f(x) = `{{:((- (x - 5))/(x - 5), "if" x - 5 < 0),((x - 5)/(x - 5), "if" x - 5 > 0):}`
f(x) = `{{:(-1, "if" x < 5),(1, "if" x > 5):}`
From the graph x = 5 curve does not intersect the line x = 5
∴ The value of the function y = f(x) does not exist at x = 5.
∴ The `lim_(x -> 5) |x - 5|/(x - 5)` does not exist.
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