Question

limits help

Answer 1

\[\lim_{x \rightarrow 1}\frac{ 2x }{ 3x^2-3x }\]

Answer 2

simplify as much as possible first, what do you get?

Answer 3

2/3x-3

Answer 4

or even a step further, \[\frac23\frac1{x-1}\]

Answer 5

ok

Answer 6

try taking the limit from each side:\[\lim_{x\to1^+}\frac23\frac1{x-1}=\frac23\lim_{x\to1^+}\frac1{x-1}=?\\\frac23\lim_{x\to1^-}\frac1{x-1}=\]

Answer 7

dont bot geive me undefined?

Answer 8

they do, but even more, in the right hand limit, because x>1, the denominator is positive, so we have\[\frac23\lim_{x\to1^+}\frac1{x-1}=+\infty\]while in the left hand limit, because x<1, the denominator is negative, giving\[\frac23\lim_{x\to1^+}\frac1{x-1}=-\infty\]so the limit itself does not exist, as the right and left hand limits both diverge to different values

Answer 9

typo, last line should read\[\frac23\lim_{x\to1^-}\frac1{x-1}=-\infty\]

Answer 10

so it doesnt exist

Answer 11

not at all, nope