Question

RATE OF CHANGE Q:
http://prntscr.com/a3sklv (Wondering if I can simplify any farther than this?)

Process: \[f(t)=\sqrt{2t}\rightarrow t=9,t=9+h\]\[\frac{f(9+h)-f(9)}{9+h-9}=\frac{\sqrt{2(9+h)}-\sqrt{2(9)}}{h}=\frac{\sqrt{18+2h}-\sqrt{18}}{h}\]

Answer 1

o_o so many people!! Hello everyone :-)

Answer 2

multiply by
\[\frac{ \sqrt{18+2h}+18 }{ \sqrt{18+2h}+18 }~and~simplify\]

Answer 3

I wrote it down but I'm not sure where to go from here, I'm sorry :-(
Should I do FOIL?

Answer 4

numerator is
\[\frac{ \sqrt{18+2h}-18 }{ h } \times \frac{ \sqrt{18+2h} +18}{ \sqrt{18+2h}+18 }=\frac{ \left\{ \left( \sqrt{18+2h} \right)^2-18^2 \right\} }{ h \left( \sqrt{18+2h}+18 \right) }\]

Answer 5

Ok, I got this: \[\frac{(18+2h)-18(\sqrt{18})}{h(\sqrt{18+2h})-18h}\]

Answer 6

Oh, did I get the right result? :-(

Answer 7

because f(9) = sqrt(2•9) right

Answer 8

i missed square root on 18
multiply by
\[\frac{ \sqrt{18+2h}-\sqrt{18} }{ h }\times \frac{ \sqrt{18+2h}+\sqrt{18} }{ \sqrt{18+2h} +\sqrt{18}}=?\]

Answer 9

Ok, I got \[\frac{(18+2h)-18}{h(\sqrt{18+2h})-\sqrt{18}h}\]

Answer 10

Oops. that can simplify more:\[\frac{2h}{h(\sqrt{18+2h}-\sqrt{18})}=\frac{2}{\sqrt{18+2h}-\sqrt{18}}\]Is this right?

Answer 11

@surjithayer ??

Answer 12

write + sign in the denominator.

Answer 13

Oh yeah, sorry! Thank you :-)
@surjithayer so is it right other than the incorrect sign?

Answer 14

yes is right but you can rationalizing again the denominator for eliminate the radicals from there - do you know it how ?

Answer 15

@jhonyy9 yes, well not exactly in this case because of the + sign...

Answer 16

yes this is indifferent than there is plus or minus you can eliminate the radicals from denominator like will be more acceptably - i think

Answer 17

Do I just multiply by the conjugate? @jhonyy9

Answer 18

yes beacuse than will get a^2 -b^2 what will result without radicals in denominator - yes ?

Answer 19

uh.
not exactly sure what you said there, but yes, non-radical denominator?

Answer 20

so this is what mean rationalize the denominator - or not ?

Answer 21

np

Answer 22

do you can ending it now sure easy - yes ?

Answer 23

I got \[\frac{\sqrt{2(9+h)}-3\sqrt{2}}{h}\] Yes?

Answer 24

how is this exactly - can you rewrite it please from what you start

Answer 25

2
------------------- =
sqrt(18+2h) +sqrt18

right ?

Answer 26

Yes. I multiplied by conjugate then simplified

Answer 27

multiplied by ( (sqrt18 +2h) -sqrt18 ) - yes ?

Answer 28

The conjugate is just the numerator but switch the signs, yes?

Answer 29

2((sqrt(18 +2h) -sqrt18) sqrt(18+2h) -sqrt18
--------------------- = -------------------
18+2h -18 h

you have got this result ?

Answer 30

Yes

Answer 31

so than is right sure

Answer 32

good luck

bye

Answer 33

hmm I am not sure who to give medal to now haha

Answer 34

nvm, he left

Answer 35

if you again rationalise you will get h again in the denominator

Answer 36

Yes o-o