Question

Please Help...
Evaluate the limit if it exists...

Answer 1

\[\lim_{h \rightarrow 0} (\sqrt{9+h} - 3)/ h\]

Answer 2

sub in h=0

Answer 3

@jfry13

Answer 4

that get 0

Answer 5

0/0

Answer 6

1/6

Answer 7

can you explain how you got 1/6

Answer 8

I can try to explain let me play with the slow equation thingy some

Answer 9

Well since both the numerator and denominator are 0 then you can use l'hopital's rule, which says you can differentiate both the numerator and denominator and get the same limit

Answer 10

The denominator is just h, so that differentiates to simply 1 (with respect to h). The numerator differentiates to 1/(2 sqrt[9+h]). If you sub in h=0 you get 1/(2 sqrt(9)), or 1/(2*3) which is 1/6.

Answer 11

or you can try rationalizing the numberator, by multiplying and dividing by the conjugate \(\sqrt{9+h}+3\)

Answer 12

\[\sqrt{9+h}-3 x \frac{ \sqrt{9+h}+3 }{ \sqrt{9+h}+3 }\]

Answer 13

maybe that will help some as all you are doing is multiplying the equation by (1) so as you simplfiy things stuff starts to cancel.

Answer 14

im still unsure of how 1/6 was reached

Answer 15

Im writing it down and it might make more sense. >.< just need to scan and insert it

Answer 16

OK Thank you

Answer 17

Ok I am scanning it now and will upload to better explain

Answer 18

\[\frac{ \sqrt{9+h}-3 }{ h }\times \frac{ \sqrt{9+h}+3 }{ }\]

Answer 19

\[\sqrt{9+h}+3\] denominator meant to be that.

Answer 20

You would get.
\[\frac{ 9+h-9 }{ h \sqrt{9+h}+3h }=\frac{ h }{ h(\sqrt{9+h}+3) }\]

Answer 21

see if this helps

Answer 22

looks like I uploaded it upside down tho lol but just stand on your head

Answer 23

\[=\frac{ 1 }{ \sqrt{9+h}+3 }\]
Now let h=0

Answer 24

You get 1/6

Answer 25

I understand it now. Thank you!

Answer 26

mhmm