Question

find the limit as h approaches 0:
f(13+h) - f(13) divided by h
if f(x) = ³√1695 - 8x^2

Answer 1

\[ ³√1695 - 8x^2\] ?

Answer 2

seems unlikely... missing something?

Answer 3

\[\lim_{h \rightarrow 0}\frac{ \sqrt[3]{1695 - 8x^2} -7 }{ h } \]

Answer 4

k

Answer 5

same gimmick as with a square root, rationalize the numerator, but this time instead of using
\[(a-b)(a+b)=a^2-b^2\] you have to use
\[(a-b)(a^2+ab+b^2)=a^3-b^3\] so it is a pain in the arse

Answer 6

the answer is \[\frac{ -208 }{ 147 }\] i want to figure what to do to get it.

Answer 7

o i see

Answer 8

have fun
but you can do it
use \(a=\sqrt[3]{1695-8x^2}\) and \(b=7\)

Answer 9

thanks

Answer 10

\[\lim_{h \rightarrow 0} \frac{ f(13 + h) - f(13) }{ h }\] this is the original question btw

Answer 11

if f(x) is \[\sqrt[3]{1695 - 8x^2}\]

Answer 12

what is \(f(13)\)?

Answer 13

\[\sqrt[3]{1695 - 8x^2} \] with 13 plugged in, which equals 7

Answer 14

ok then you can start with
\[\frac{\sqrt[3]{1695-8(13+h)^2}-7}{h}\]\]

Answer 15

yep

Answer 16

you can leave it in this form, or you can write
\[\sqrt[3]{343-h^2-208h}-7\]

Answer 17

who gave you this problem? this really sucks
unless you are supposed to use a shortcut, namely recognize this as the derivative and evaluate

Answer 18

university online homework

Answer 19

mathXL

Answer 20

do you know how to take a derivative? because then it it would be not so hard
but if you do not, then there is a ton of work to be done

Answer 21

i do know, im not sure if it would give me the answer im supposed to get

Answer 22

ill try taking the derivative

Answer 23

this is the derivative of
\[\sqrt[3]{1695-8x^2}\] evaluated at \(x=13\)

Answer 24

so if you can take the derivative, then plug in 13, you will get your answer

Answer 25

just to finish quick derivative is
\[\frac{-16x}{3(1695-8x^2)^{\frac{2}{3}}}\]

Answer 26

by the chain rule and power rule
replace \(x\) by 13 and you should get your answer
this is a much snappier way then doing it by hand

Answer 27

ohh ok thanks!

Answer 28

yeah i think i got the same

Answer 29

yw