Question

I have a function f(x) = sqrt(5x+1) and I'm trying to find f'(a) using the definition:

lim h->0 f(a+h) - f(a)/h

I'm having a hard time simplifying the expression. Help!

Answer 1

Okay. You have:
\[\lim_{h \rightarrow 0}\frac{\sqrt{5x+5h+1}-\sqrt{5x+1}}{h}\]
Now let me look at it :P

Answer 2

I got it :P I think.
Multiply the top and bottom by:
\[\sqrt{5x+5x+1}+\sqrt{5x+1}\]
After that, see if you can figure it out :P

Answer 3

lim┬(h→0)⁡〖([√(5(a+h)+1)]- [√(5a+1)])/h〗

Answer 4

rationalize!

Answer 5

ratiaonlize the numerator!

Answer 6

multiply by our favorite thingy the conjugate of the top

Answer 7

if we do it to the top we have to do it the bottom

Answer 8

malevolence has it . you have to do some algebra, but the numerator will be
\[5x+5h+1-(5x+1)=5h\]

Answer 9

the h will cancel because u have one on bottom too

Answer 10

Then you get:
\[\lim_{h \rightarrow 0}\frac{5x+5h+1-5x-1}{h(\sqrt{5x+5h+1}+\sqrt{5x+1})}\]
Everything cancels in the top leaving a 5h. Divide out the h in the top and bottom. Then you take the limit and the denominator becomes:
\[\sqrt{5x+1}+\sqrt{5x+1}=2\sqrt{5x+1}\]
Giving!
\[\frac{5}{2\sqrt{5x+1}}\]

Answer 11

and the denominator will be
\[h(\sqrt{5x+5h+1}+\sqrt{5x+1})\]

Answer 12

appletastic!

Answer 13

cancel the h wow! nice latex malevolence!

Answer 14

I was trying to type quickly :P Got you and myininaya jumping down my throat xPPP

Answer 15

lol

Answer 16

\[\color{green}{\text{appletini}}\]

Answer 17

omg satellite you will not believe this but malevolence corrected me earlier

Answer 18

latex color race this fall

Answer 19

i tried to tell him it was just a typo like you always say

Answer 20

\[\color{blue}{\text{you probably needed it}}\]

Answer 21

\[\huge\int\limits x^2dx\]

Answer 22

when i do it: typo
when you do it: error

Answer 23

wow thats big

Answer 24

LARGE!

Answer 25

the satellite signal is out! come on i will be your sidekick

Answer 26

\[\huge\int\limits \int\limits_D \int\limits \frac{P(z)}{Q(z)}dV\]

Answer 27

\[\huge\text{mine's bigger}\]

Answer 28

\[\huge\color{red} {redder}\]