Question

what is the limit of ln(x-5) as x approaches 5 from the right

Answer 1

Do you know the graph of ln(x)?

Answer 2

graph of ln(x)

Answer 3

The use the construct that f(x-a) is the function f(x) shifted to the right along the x-axis. This means that ln(x-5) has similar behavior to ln(x), just shift intercepts and asymptotes to the right

Answer 4

Also you should probably note you can't take the log of a negative number

Answer 5

So looking at the graph of ln(x) what happens a x->0?

Answer 6

Is that relevant here, as it approaches 5 from the right, not the left.

Answer 7

from d definition, we say there should be some inteval I such that out epsilon delta definition applies, therefore the question is whether such an interval can be obtained from the plot?

Answer 8

Correction , as x->0 from the right.