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Unformatted text preview: 3 5 ) Solution: cot(arcsin3 5 ) =4 / 3 (see triangle below) 5 43 θ 3. [3 pts] lim x →∞ arctan( e x ) Solution: x → ∞ ⇒ e x → ∞ ⇒ arctan( e x ) → π/ 2 ⇒ lim x →∞ arctan( e x ) = π/ 2 Quiz 3, Page 2 of 2 February 5, 2008 4. [3 pts] Compute the derivative of y = tan1 (cosh x ). Solution: y = 1 1 + (cosh x ) 2 · (cosh x ) = sinh x 1 + cosh 2 x (Chain Rule) 5. [3 pts] Z 1 1 / 2 dx √ 1x 2 arcsin x Solution: Let u = arcsin x , then du = dx/ √ 1x 2 , and Z 1 1 / 2 1 arcsin x dx √ 1x 2 = Z π/ 2 π/ 6 du u = ln u ± ± ± ± ± π/ 2 π/ 6 = ln( π/ 2)ln( π/ 6) = ln( π/ 2 π/ 6 ) = ln 3...
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 Spring '09
 EGCDD
 Calculus, Bacteria, 1917, Inverse trigonometric functions, Hyperbolic function

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