The discussion centers around evaluating the limit \(\lim_{x\rightarrow 1} {\frac{\sqrt[3]{x}-1}{\sqrt{x}-1}}\) without using L'Hopital's rule, as the problem is presented prior to the introduction of that method in the textbook.
Several participants have contributed suggestions for alternative approaches to the limit, including algebraic simplifications and factorizations. The discussion is ongoing, with helpful insights being shared, but no consensus has been reached on a single method.
The problem is framed within the constraints of not using L'Hopital's rule, prompting participants to consider foundational algebraic techniques instead.
cambo86 said:Homework Statement
<br /> \lim_{x\rightarrow 1} {\frac{\sqrt[3]{x}-1}{\sqrt{x}-1}}<br />
I can do this very easily using L'Hopital's rule but in the textbook I'm going through it is a problem given before L'Hopital's rule is taught. Is there a way of doing this without using L'Hopita'ls rule?
Do you know how to factor the difference of squares and the difference cubes ?cambo86 said:Homework Statement
<br /> \lim_{x\rightarrow 1} {\frac{\sqrt[3]{x}-1}{\sqrt{x}-1}}<br />I can do this very easily using L'Hopital's rule but in the textbook I'm going through it is a problem given before L'Hopital's rule is taught. Is there a way of doing this without using L'Hopita'ls rule?