Question

Find the Limit of

lim =((1/x)-(1/5))/x-5
X=>5

Answer 1

\[\lim_{x \rightarrow 5}=(1/x)-(1/5))/x-5\]

Answer 2

have you covered l'hopitals rule ?

Answer 3

no not at all, but i figured out what I did wrong, if you don't mind. What exactly is the rule?

Answer 4

if you havent covered you can solve it other way , just lhopitals rule makes it easier
it is :
if limit is of form 0/0 or infinity/infinity , you take the derivative of numerator and denominator and the limit wont change but might make it easier to solve

Answer 5

what did u get for result ?

Answer 6

\(\bf \lim_{x \rightarrow 5}
\cfrac{
\frac{1}{x} - \frac{1}{5}
}{
x-5
} \implies
\cfrac{\frac{5-x}{5x}
}{x-5} \implies \cfrac{5-x}{5x} \times \cfrac{1}{x-5}\\
\lim_{x \rightarrow 5}\cfrac{-(x-5)}{5x} \times \cfrac{1}{x-5}\)

Answer 7

\[\lim_{x \rightarrow 5} \frac{ \frac{ 5-x }{ 5x } }{ x-5 }\rightarrow \frac{ -1 }{ 5x }=\frac{ -1 }{ 25 }\]

Answer 8

sorry @jdoe0001 I didn't see your reply

Answer 9

np, it just came about 2secs before yours :)