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Calculus I                                                        Quiz #10                         November 23, 2004

Name____________________                   R.  Hammack                             Score ______
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(1)  
(a)  cos^(-1)(-1/2^(1/2)) =(3π)/4
(b)   sin ( tan^(-1)(x) ) =OPP/HYP = x/(1 + x^2)^(1/2)   [Graphics:HTMLFiles/Q10F04A_5.gif]


(c)   Sketch the graph of   y = tan^(-1)(x).  Please indicate any asymptotes.

[Graphics:HTMLFiles/Q10F04A_7.gif]


(2)  f(x) = ln ( sin^(-1)(x) )

(a)    f '(x) = 1/sin^(-1)(x) 1/(1 - x^2)^(1/2) = 1/(sin^(-1)(x) (1 - x^2)^(1/2))


(b)     f ' (1/2) =1/(sin^(-1)(1/2) (1 - (1/2)^2)^(1/2)) = 1/(π/6 (1 - 1/4)^(1/2)) = 1/(π/63/4^(1/2)) = 1/(π/63^(1/2)/2) = 12/(π3^(1/2)) = (43^(1/2))/π



(3)  f(x) = tan^(-1)(x^(1/2))

(a)    f '(x) = 1/(1 + (x^(1/2))^2) 1/(2x^(1/2)) = 1/(2x^(1/2) (1 + x))


(b)     f ' (4) =1/(24^(1/2) (1 + 4)) = 1/20