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- Feb 6, 2014

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- Feb 6, 2014

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- Jan 30, 2012

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[GRAPH]5wib4rocqz[/GRAPH]

the area is

\[

\int_{0}^2(-(x-2)^3+2)-(x^2-2)\,dx

\]

Limits of the form $\lim_{n\to\infty}f(n)^{g(n)}$ are usually easier to compute when the function is represented as $e^{g(n)\ln(f(n))}$. Which ways of finding limits do you know?

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- Feb 6, 2014

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By substitution, or expanding, or Hospital rule i suppose.

[GRAPH]5wib4rocqz[/GRAPH]

the area is

\[

\int_{0}^2(-(x-2)^3+2)-(x^2-2)\,dx

\]

Limits of the form $\lim_{n\to\infty}f(n)^{g(n)}$ are usually easier to compute when the function is represented as $e^{g(n)\ln(f(n))}$. Which ways of finding limits do you know?

Thank you

- Jan 30, 2012

- 2,502

I think, the easiest way is to expand $\ln(1+x)$ as $x+o(x)$, but l'Hospital's rule works too. Recall that to apply the rule you need to represent the function as a ratio of two functions that tend both to zero or both to infinity.By substitution, or expanding, or Hospital rule i suppose.