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problems-10-15-07 copy 4

problems-10-15-07 copy 4 - x 2(l x x(5 Find a real number Î...

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Still More Problems (1) Express the following as a single logarithm: ln(cos x ) + 1 2 ln(1 + x 2 ) - ln(sin x ) (2) Find the exact values of the following expressions: e - 2 ln 5 , ln(ln e e 10 ) , log 2 6 - log 2 15 + log 2 20 . (3) Solve the following equations for x : ln(5 - 2 x ) = - 3 , e 3 x +1 = 15 , ln(ln( x - 1)) = 1 . (4) Calculate the derivatives of the following functions. Do not simplify. (a) sin( e t ) + e sin t (b) 1 ln x (c) e x 1 + x (d) cos( e x + ln x ) (e) ln ± 1 x ² (f) e e x (g) ln(ln x ) (h) e e e x (i) 1 + xe - x (j) ln(1 + e x ln x ) (k) ln ³ e x e cos x + 5
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Unformatted text preview: x 2 (l) x x (5) Find a real number Î» such that if y = e Î»x , then 2 y Â±-y = y Â± . (6) If f ( x ) = e 2 x , what is f (100) ( x )? (7) A rectangle has two sides on the positive x- and y-axes, and one vertex V on the curve y = e x . If V moves so that y increases at 1 / 2 units per second, how fast is the area of the rectangle changing when y = 3?...
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