Question

limit help

Answer 1

whats the question>

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

Oh now you say you were given that.

Answer 6

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

Answer 7

x+7=t^3

as x ---> 1

t ----> 2

Answer 8

Factorise

Answer 9

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

Answer 10

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

Answer 11

No you sub the x on the numerator as well.

Answer 12

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

Answer 13

\[t^3=x+7\]
make x the subject.
\[x=t^3-7\]

Answer 14

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

Answer 15

oh now i get it. pass the duh stamp

Answer 16

Now you can get rid of that denominator.

Answer 17

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

Answer 18

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

Answer 19

got it thank you!