Question

can some one pls explain this to me:
The limit as h goes to 0:
((sqrt(3+h)-sqrt(3)))/h
represents the derivative of a function f at a number c. Determine f and c.
Thank you!

Answer 1

sqrt(x) derives to 1/2sqrt(x)

Answer 2

\[\frac{\sqrt{x+h}-\sqrt{x}}{h}=\frac{\sqrt{x+h}}{h}-\frac{\sqrt{x}}{h}\] cant recall it really

Answer 3

maybe it the \[\frac{f(b)-f(a)}{b-a}\]version

Answer 4

ueah; i think its has to do with the conjugate

Answer 5

\[\frac{\sqrt{x+h}-\sqrt{x}}{h}*\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}\]

Answer 6

tryig to type and math at the same time... messed it up lol

Answer 7

haha - no worries< Im going through it all

Answer 8

what does the q mean when it asks for f and c? that;s my real issue

Answer 9

that 2sqrt(garbage) up top is not spose to even be there; when you multiply conjugates there is no middle term :)

Answer 10

q?

Answer 11

question
\

Answer 12

oh; its asking for the derivative of the function and the value used which is 3 n this case

Answer 13

I calc'ed it hoping that;s what it meant :-)

Answer 14

what do you mean by value?

Answer 15

\[\frac{h}{h(\sqrt{x+h}+\sqrt{x})}\]

\[\lim_{h->0}\ \frac{1}{\sqrt{x+h}+\sqrt{x}}\ =\frac{1}{\sqrt{x}+\sqrt{x}}\]

Answer 16

you see how they begin with 3+h instead of x+h? c = 3

Answer 17

f(c) = \(\frac{1}{2\sqrt{c}}\) when c = 3

Answer 18

yes, i see that

Answer 19

so c is the x value?

Answer 20

yes; c usually denotes the term of the limit as in \(\lim_{x->c}\)

Answer 21

oh, I see!

Answer 22

to determine the f or derivative would I be required to plug in the 0 at the end? since it is h goes to 0?

Answer 23

c = ssqrt3

Answer 24

\[\lim_{x->3}\frac{\sqrt{x+h}-\sqrt{x}}{h}=\frac{1}{2\sqrt{x}}=\frac{1}{2\sqrt{3}}\]

Answer 25

here's the answer

Answer 26

f(x)=sqrtx
at the point c = 3

Answer 27

well, yeah; sqrt(x) derives to; 1/2sqrt(x)

Answer 28

i try to do those mathlab type websites where they give you practice problems ...... i loathe them. they never seem to be able to say exactly what it is they want you to do lol

Answer 29

that was my issue with this question....

Answer 30

Thanks for your help!

Answer 31

:) just swear at the computer monitor and click next :)

Answer 32

so to calc f I am saying as x goes to 3

Answer 33

hahahaha! I wish I could. I am changing careers and they wont take my highschool calc classes ( over a decade ago) so im back in calc and have to do well

Answer 34

the question asked, in hindsight, what function are they deriving and what did they use for 'c'

f(x) = sqrt(x) and c = 3

Answer 35

thanks!

Answer 36

that was a really backwards way to ask such an easy question?

Answer 37

thanks a ton amistre! you are awesome!
off to sleep, have to wake up early to trade oil :-)