Question

lim x --> 1

Answer 1

\[\lim_{x \rightarrow 1} (\sqrt{x}-1) / (\sqrt[3]{x}-1)\]

Answer 2

\[\lim_{x \rightarrow 1} {x^{1/2} -1 \over x^{1/3} -1} \]

Answer 3

* watches in fathom *

Answer 4

nice question

Answer 5

use l'Hospital's rule to compute this indeterminate form

Answer 6

let x = z^6, when x -> 1, z -> 1\[\lim_{z \rightarrow 1} \frac{z^3 - 1}{z^2 - 1}\]\[\lim_{z \rightarrow 1} \frac{\left( z - 1 \right)\left( z^2 + z + 1 \right)}{(z - 1)(z + 1)}\]\[\lim_{z \rightarrow 1} \frac{z^2 + z + 1}{z + 1}\]

Answer 7

Great! I checked it on function. its 1.5 as you reached exraven
thanks

Answer 8

Using l"hospital's rule and taking the limit gives,