10thsol - Calculus 119 10th Week1 Recall: 1. 2. 3. 4. 5. 6....

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Calculus 119 10th Week 1 Recall: 1. sin - 1 x = arcsin x = y sin y = x where - π 2 y π 2 2. cos - 1 x = arccos x = y cos y = x where 0 y π 3. tan - 1 x = arctan x = y tan y = x where - π 2 y π 2 4. csc - 1 x = arccsc x = y ( | x | ≥ 1) csc y = x where 0 < y π 2 or π < y 3 π 2 5. sec - 1 x = arcsec x = y ( | x | ≥ 1) sec y = x where 0 < y π 2 or π < y 3 π 2 6. cot - 1 ( x ∈ < ) cot y = x where 0 < y < π 1. (a) tan - 1 (tan 2 π 3 ) = tan - 1 (tan( 2 π 3 + )) where k N = tan - 1 (tan - π 3 ) = - π 3 (b) sin(cos - 1 ( - 1 3 ) =? Let cos - 1 ( - 1 3 ) = y cos y = - 1 3 sin( cos - 1 ( - 1 3 ) sin y = 1 - (cos y ) 2 = 1 - ( - 1 3 ) 2 = 8 9 2. f 0 ( x ) = 1 q 1 - ( 2 x - 1 3 ) 2 ± 2 3 ² 3. By using implicit diferentiation 1 1 + ³ 2 x y ´ 2 d ( 2 x y ) dx = πy 2 + πx 2 y dy dx y 4 1 1+ ( 2 x y ) 2 2 y +2 x dy dx y 2 = πy 2 + πx 2 y dy dx y 4 At (1 , 2) 1 1+ ( 2 2 ) 2 2 . 2+2 dy dx 2 2 = π 2 2 + π 1 . 2 . 2
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10thsol - Calculus 119 10th Week1 Recall: 1. 2. 3. 4. 5. 6....

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