Question

Limits question

Answer 1

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

Answer 2

Try simplifying the numerator.

Answer 3

\[\frac{1}{3} - \frac{1}{x} = ?\]

Answer 4

\[\frac{ x-3 }{ 3x }\]

Answer 5

yes now put 3 it is now defined
it does not have 0/0 form

Answer 6

\(\frac{ x-3 }{ 3x} \) is correct, now we simplify by (x-3) since we have it in the numerator and denominator. What do you get ?

Answer 7

Now you are at this point
\[\lim_{x \rightarrow \infty }\frac{ \frac{ x-3 }{ 3x } }{ x-3 }\]
you can combine the denominators
\[\lim_{x \rightarrow \infty }\frac{ x-3 }{ 3x(x-3) }\]
notice the x-3 will cancel in the numerator and denominator

Answer 8

the limits should be as x approaches 3* didnt see that