Finding limit using l'hôspital

Question

We're supposed to find the following limits by applying l'Hôspital rule:

$$ \lim_{x \to \infty} x^{sin(1/x)} $$ My idea was to view the limit as y, then evaluate ln(y). However, I wasn't sure how we could rewrite this to a fraction.

Hint: What is the definition of $x^y$? – PhoemueX Nov 22 '14 at 20:32 — PhoemueX, Nov 22 '14 at 20:32

score 2 · Accepted Answer · answered Nov 22 '14 at 20:35

2

HINT. $$e^{\frac{\ln x}{\sin^{-1} (1/x)}}=e^{-\frac{\ln t}{\sin^{-1} t}}\underbrace=_H e^{\frac{\sin t}{t}\frac{\sin t}{\cos t}}\rightarrow 1 \ \ \ (t\rightarrow 0)$$

answered Nov 22 '14 at 20:35

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Finding limit using l'hôspital

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