handout_11_09

# handout_11_09 - ^ L'HOPITAL'S RULE 1 Find lim e3t 1 t0 t 2...

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L’H ˆ OPITAL’S RULE 1. Find lim t 0 e 3 t - 1 t . 2. Find lim x 1 ln x sin πx . 3. What is lim x 0 sin 2 ( x ) x 2 - x 3 ? 4. Last night, I was trying to compute lim x 0 sin(3 x ) x 2 + x . The numerical evidence does not seem to agree with my conclusion. What is going on? Repeated application of l’Hˆopital’s rule gives: lim x 0 sin(3 x ) x 2 + x = lim x 0 3 cos(3 x ) 2 x + 1 = lim x 0 - 9 sin(3 x ) 2 = 0 . A table of values gives: x sin(3 x ) x 2 + x 0 . 01 2 . 969 - 0 . 01 3 . 029 0 . 001 2 . 9969 - 0 . 001 3 . 003 0 . 0001 2 . 99969 - 0 . 0001 3 . 0002 Date : November 9, 2009. 1

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5. Compute lim x 0 x arctan(4 x ) . 6. Calculate lim x 0 +
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## This note was uploaded on 03/27/2012 for the course MATH 1a taught by Professor Benedictgross during the Fall '09 term at Harvard.

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handout_11_09 - ^ L'HOPITAL'S RULE 1 Find lim e3t 1 t0 t 2...

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