Question

Please help me with this problem.
Also, don't use l'hopital's rule.

Answer 1

Find \[\lim_{\Delta \rightarrow 0}\frac{ f(x+\Delta x)-f(x) }{ \Delta x }\]
When
\[f(x)=\sqrt{x}\]

Answer 2

lets get rid of that stupid \(\Delta\) because it is too hard to write, and replace it by the usual \(h\) and write
\[\frac{\sqrt{x+h}-\sqrt{x}}{h}\]

Answer 3

the steps are rationalize the numerator,
cancel,
replace \(h\) by \(0\)

Answer 4

try it, if you get stuck let me know
a hint is to leave the denominator in factored form, don't multiply out

Answer 5

So it's\[\frac{ \sqrt{x} }{ 2x }\]

Answer 6

I had this answer, but I wasn't really sure if it's a valid one.

Answer 7

oooh i see what you wrote

Answer 8

yeah i guess you are right, but really you want to leave it as
\[\frac{1}{2\sqrt{x}}\]

Answer 9

Alright then. Well thank you for taking your time in helping me with this problem, Satellite.

Answer 10

yw