Question

Evaulate the limits
lim ((1/s)-(1/6))/(s-6)
s->6

Answer 1

Typing it in latex makes it a bit unclear, so I'll do my best typing it normally:
lim s→6 [1/s - 1/6] / (s - 6)

The numerator's fractions can be combined to get
(6 - s)/(6s).

And this over (s - 6), so you have
lim s→6 [(6 - s)/(6s)] / (s - 6)

Note that s - 6 = -(6 - s), so you have
(-1) lim s→6 [(6 - s)/(6s)] / (6 - s)

You can probably see where this is going.

Answer 2

mmmmm

Answer 3

I'm not sure why it should be any less clear when formatted in LaTeX. It is a pain to type, though!

\[\lim_{s\rightarrow 6 } \frac{(\dfrac{1}{s}-\dfrac{1}{6})}{s-6}\]Establish a common denominator for the numerator fractions
\[\lim_{s\rightarrow 6 } \frac{(\dfrac{1*6}{s*6}-\dfrac{1*s}{6*s})}{s-6} = \lim_{s \rightarrow 6} [\frac{6-s}{6s}*\frac{1}{s-6}] = \lim_{s \rightarrow 6} [\frac{-1(s-6)}{6s}*\frac{1}{s-6} ] =\]and hopefully you can do the rest!

Answer 4

Yeah, I didn't like how small the s turns out under the limit.