## anonymous 3 years ago limit help

1. perl

whats the question>

2. anonymous

$\lim_{x \rightarrow 1}\frac{ x-1 }{ \sqrt[3]{x+7}-2 }$

3. anonymous

I am having trouble with this equation we are given the hint make the substation x+7=t^3

4. anonymous

Rationalise the denominator by multiplying by $\frac{ \sqrt[3]{(x+7)^2}+2 }{ \sqrt[3]{(x+7)^2}+2 }$

5. anonymous

Oh now you say you were given that.

6. anonymous

$=\frac{ t^3-7-1 }{ t-2 }$

7. anonymous

x+7=t^3 as x ---> 1 t ----> 2

8. anonymous

Factorise

9. anonymous

And you can get rid of the denominator. Once you do that. Sub back the x's.

10. anonymous

so when i make the sub I get $\lim_{x \rightarrow 1} \frac{ x-1 }{ t+2 }$ ?

11. anonymous

No you sub the x on the numerator as well.

12. anonymous

a^3 - b^3 = (a-b) (a^2 +ab + b^2

13. anonymous

$t^3=x+7$ make x the subject. $x=t^3-7$

14. anonymous

Now sub the x on the numerator with t^3-7

15. anonymous

oh now i get it. pass the duh stamp

16. anonymous

Now you can get rid of that denominator.

17. anonymous

Once you do that, remember to replace the t's with $\sqrt[3]{x+7}$

18. anonymous

and then you can then sub in x=1 to find the limit.

19. anonymous

got it thank you!

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