Question

What is the limit as x approaches 2 of the function (1/x - 1/3)/(x-3)?

The fractions part of the problem made me confused and get the wrong answer.

Answer 1

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

Answer 2

what would you get for.. say \(\bf \cfrac{1}{x}-\cfrac{1}{3}?\)

Answer 3

You'd get 0 when you subsitute 3 for x.

Answer 4

well.. I meant the numerator only :)

Answer 5

Oh ok. :D

Answer 6

The only thing I don't get is that I got 0 both in the numerator and the denominator. Not sure what to do next.

Answer 7

right... one sec
bear in mind that \(\bf a-b \iff -(b-a)\)

one sec

Answer 8

Ok

Answer 9

\(\bf \lim\limits_{x\to 3}\ \cfrac{\frac{1}{x}-\frac{1}{3}}{x-3}
\\ \quad \\
\cfrac{\frac{3-x}{3x}}{x-3}\implies \cfrac{\frac{3-x}{3x}}{\frac{x-3}{1}}\implies \cfrac{3-x}{3x}\cdot \cfrac{1}{x-3}
\\ \quad \\
\cfrac{3-x}{3x(x-3)}\implies \cfrac{{\color{brown}{ -\cancel{(x-3)}}}}{3x\cancel{(x-3)}}\)

Answer 10

Oh, now I see what I was supposed to do! Thank you very much!

Answer 11

yw