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Unformatted text preview: Math 119 Recitation 12
December 5, 2006
1. Differentiate (a) y = arcsin 1 - x2 (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 ( 2x ) - x = 0 at the point (1, 2). y y2 3. Evaluate the integrals (a) (b) (c)
2 dx -1 x2 +2 dx x x2 -49 sinh(2 - 3x) dx 4. Evaluate the limits (a) limx0 (b) (c)
arctan x (with x limx0 arcsin3x-x x 2 cos x-1 limx 1-tan2 (x) 4 and without L'Hospital's rule) x+1 (d) limx ( x-1 )x 1 (e) limx1+ ( x-1 )ln x 4 (f) limx- (1 - 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. (b) Find an expression for the population after t hours. (c) Find the number of cells after 5 hours. (d) Find the rate of growth after 5 hours. (e) When will the population reach 200,000. 1 6. A thermometer is taken from a room where the temperature is 20 C to the outdoors where the temperature is 5 C. After one minute the thermometer reads 12 C. (a) What will be the reading on the thermometer be after 1 more minute. (b) When will the thermometer read 6 C. 2 ...
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This note was uploaded on 04/30/2010 for the course MATHEMATIC MATH 119 taught by Professor Tor during the Spring '10 term at Middle East Technical University.
- Spring '10