## iop360 Group Title find the limit as h approaches 0: f(13+h) - f(13) divided by h if f(x) = ³√1695 - 8x^2 one year ago one year ago

1. Algebraic! Group Title

$³√1695 - 8x^2$ ?

2. Algebraic! Group Title

seems unlikely... missing something?

3. iop360 Group Title

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

4. Algebraic! Group Title

k

5. satellite73 Group Title

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

6. iop360 Group Title

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

7. iop360 Group Title

o i see

8. satellite73 Group Title

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

9. iop360 Group Title

thanks

10. iop360 Group Title

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

11. iop360 Group Title

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

12. satellite73 Group Title

what is $$f(13)$$?

13. iop360 Group Title

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

14. satellite73 Group Title

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

15. iop360 Group Title

yep

16. satellite73 Group Title

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

17. satellite73 Group Title

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

18. iop360 Group Title

university online homework

19. iop360 Group Title

mathXL

20. satellite73 Group Title

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

21. iop360 Group Title

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

22. iop360 Group Title

ill try taking the derivative

23. satellite73 Group Title

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

24. satellite73 Group Title

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

25. satellite73 Group Title

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

26. satellite73 Group Title

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

27. iop360 Group Title

ohh ok thanks!

28. iop360 Group Title

yeah i think i got the same

29. satellite73 Group Title

yw