Question

a=4, f(x)= |x-4|/X-4 find lim and x goes to a+

Answer 1

Because the question asks for a right-hand limit, both the numerator and denominator will always be the same positive value, therefore the limit is 1.

Answer 2

\[x>4=>|x-4|=x-4, x<4=>|x-4|=-(x-4)\]
\[\lim_{x \rightarrow 4^-}\frac{-(x-4)}{x-4}=-1, \lim_{x \rightarrow 4^+}\frac{x-4}{x-4}=1\]
\[\lim_{x \rightarrow 4}f(x) DNE\]

Answer 3

The right hand limit is 1

Answer 4

Similarly, if it asked for a left-hand limit, then the numerator would always be positive while the denominator would always be negative, thus the limit would be -1. Just as with your previous question, this means that the "global" limit would not exist.