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# 12th - Math 119 Recitation 12 December 5 2006 1...

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Math 119 Recitation 12 December 5, 2006 1. Differentiate (a) y = arcsin 1 - x 2 (b) y = arctan 1 - x 1+ x (c) y = arctan (sin x ) (d) y = tanh (ln x ) 2. Find the tangent line to the curve arctan ( 2 x y ) - πx y 2 = 0 at the point (1 , 2). 3. Evaluate the integrals (a) 2 - 1 dx x 2 +2 (b) dx x x 2 - 49 (c) sinh(2 - 3 x ) dx 4. Evaluate the limits (a) lim x 0 arctan x x (with and without L’Hospital’s rule) (b) lim x 0 arcsin x - x x 3 (c) lim x π 4 2 cos x - 1 1 - tan 2 ( x ) (d) lim x →∞ ( x +1 x - 1 ) x (e) lim x 1 + ( 1 x - 1 ) ln x (f) lim x →-∞ (1 - 4 x ) x - 1 5. A bacteria culture grows with constant relative growth rate. After 2 hours there are 600 bacteria and after 8 hours the count is 75,000. (a) Find the initial population.

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12th - Math 119 Recitation 12 December 5 2006 1...

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