## adam32885 Group Title limit help one year ago one year ago

1. perl Group Title

whats the question>

2. adam32885 Group Title

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

3. adam32885 Group Title

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

4. Azteck Group Title

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

5. Azteck Group Title

Oh now you say you were given that.

6. Azteck Group Title

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

7. Yahoo! Group Title

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

8. Azteck Group Title

Factorise

9. Azteck Group Title

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

10. adam32885 Group Title

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

11. Azteck Group Title

No you sub the x on the numerator as well.

12. Yahoo! Group Title

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

13. Azteck Group Title

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

14. Azteck Group Title

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

15. adam32885 Group Title

oh now i get it. pass the duh stamp

16. Azteck Group Title

Now you can get rid of that denominator.

17. Azteck Group Title

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

18. Azteck Group Title

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

19. adam32885 Group Title

got it thank you!