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)`

Answer 1

`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.