EXAM1 - Math 133 Dr. Kurtz Exam 1 Name_ Section No._ TA_...

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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 2 x e y x = Quotient rule: 22 2 4 (2) ( 2) xx x ex e x y x −− ′ = Product rule: 32 21 yee x x x ′=− + (b) sin(ln(3 )) yx = 1 cos(ln(3 )) 3 3 x  ′ =   (c) (ln ) x = ln ln(ln ) x = 11 ln(ln ) ln y x =+ 1 ( l n) l n ( l n) ln x x x Alternatively, ln(ln ) ye = ln(ln ) 1 l n ( l ( l n ( l ln ln x x x x
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2. (21 pts) Evaluate the integrals. (a) sin(3 ) 6tan(3 ) 6 cos(3 ) x x dx dx x = ∫∫ cos(3 ) 3sin(3 ) ux du x dx = =− 1 62 l n c o s 3 3 du x C u  = +   (b) 3 1 ln x dx x ln dx du x = = ln 3 ln 3 13 3 22 2 0 0 (ln 3) 33 ud u u == (c) 1 1 1 0 0 11 1 2 xx xe dx e e −− + Alternatively, setting 2 2 du xdx 1 1 1 0 0 1 1 2 2 uu edu e e −= = +
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3. (14 pts) A cup of soup with an initial temperature of 180 o F cools to 120 o F after 10 minutes in a room whose temperature is 70 o F. Find the temperature of the soup after an additional 20 minutes.
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EXAM1 - Math 133 Dr. Kurtz Exam 1 Name_ Section No._ TA_...

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