Question

find the limit

Answer 1

Of?

Answer 2

\[\lim_{\Delta x \rightarrow 0^{-}} \frac{ \frac{ 1 }{ x+\Delta x } -\frac{ 1 }{ x }}{ \Delta x }\]

Answer 3

tried to simplify the numerator by cross-multiplying ?

Answer 4

\[\frac{ \frac{ x }{ x(x+\Delta x) }-\frac{ x+\Delta x }{ x(x+\Delta x) } }{ \Delta x}\]

Answer 5

The numerator would simplify to \[\frac{ -\Delta x }{ x(x+\Delta x) }\]

Answer 6

correct!!
so what gets cancelled from numerator and denominator ??

Answer 7

Oh I see that would simplify to \[\frac{ -1 }{x(x+\Delta x) }\] and since delta x is approaching zero you would get -1/x^2

Answer 8

absolutely! :D
good work!

Answer 9

Thank you!

Answer 10

welcome ^_^