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133exam1asolution

133exam1asolution - Math 133 Dr Kurtz Exam 1 Name Section...

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Math 133 Exam 1 Name___________________ Dr. Kurtz Section No.______________ TA_____________________ Instructions : Please show all of your work. Credit will not be given for answers with no supporting work. 1. (21 pts) Compute dy dx . (a) 2 1 sin x ye x ⎛⎞ = ⎜⎟ ⎝⎠ 22 2 11 (2) s i n c o s xx x e 1 x −− =− + (b) 2 ln(tan( )) y x = 2 1 sec ( )2 tan( ) y x ′ = (c) ln (ln ) x y x = l n ( l n) l n ( l yx = x ln(ln ) ln ln y 1 y =+ x ln (ln ) ln(ln ) ln ln x 1 x Alternatively, (ln )ln(ln ) x x = (ln )ln(ln ) ln 1 1 ln(ln ) ln (ln ) ln(ln ) ln ln ln x x x x x x 1 1 x x = +

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2. (21 pts) Evaluate the integrals. (a) cos(5 ) cot(5 ) sin(5 ) 11 1 ln ln sin(5 ) 55 5 x xdx dx x du uC x C u = ==+ = + ∫∫ sin(5 ) 5cos(5 ) ux du x dx = = (b) 2 3 1 ln 2 ln 2 44 3 0 0 (ln ) (ln 2) x dx x u udu == = ln dx du x = = (c) 22 2 1 0 00 (2) xx x xe dx x e dx e e −− =− + 1 1 2 2 Alternatively, substitute to get 2 2 du xdx ⎧ =− 1 0 u edu e 1 2 +
3. (16 pts) A certain unstable isotope decays according to the model dA kA dt = . If there are

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133exam1asolution - Math 133 Dr Kurtz Exam 1 Name Section...

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