L'Hopital's Rule and LimitsDate: 7 Aug 1995 08:59:44 -0400 From: Greg Sharpe Subject: Limits Find Lim [sin 3x / tan (x/3)] x->0 Date: 7 Aug 1995 09:54:14 -0400 From: Dr. Ken Subject: Re: Limits Hello! The best tool you can use in this situation is L'Hopital's rule, which says that as long as the numerator and denominator are both going to zero (or both going to positive infinity, or both going to negative infinity), we can take the derivative of the numerator and the denominator. Doing that, we get 3 * Cos(3x) 9 * Cos(3x) ___________ = ___________ Sec^2(x/3)/3 Sec^2(x/3) Plugging in zero to this fraction, the Cosine and the Secant terms both go to one, so the whole fraction goes to 9. -K |
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