Question

lim x>0 |x|/x

0
nonexistent
1
-1
none of these

Answer 1

\[\bf \lim_{x \rightarrow 0}\frac{ |x| }{ x }\]Since we have an absolute value, we can re-write the function we are taking limit of as a piecewise function. \[\bf \frac{ |x| }{ x }=1; \ for \ x>0 \ \ and \frac{ |x| }{ x }=-1; \ for \ x < 0\]So our graph looks like this:Clearly we notice that the limit from the right side is not the same as the limit from the left side:\[\bf \lim_{\ \ x \rightarrow 0^+}\frac{ |x| }{ x } \ne \bf \lim_{\ \ x \rightarrow 0^-}\frac{ |x| }{ x }\]Since the one-sided limits are not equal, the limit doesn't exist:\[\bf \therefore \bf \lim_{x \rightarrow 0}\frac{ |x| }{ x }=D.N.E\]

Answer 2

@mwixted2

Answer 3

darrn it i thought the answer was 2....

Answer 4

one more question?

Answer 5

you can make a new one.

Answer 6

its with the same function, just determining whether it is continuous at x=0