# Exam3 review - x C y cos-= and the initial condition 1 3 =...

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Calculus Review for Exam #3, fall 2005 1. a. Evaluate + - dx x x x 2 2 csc cos 3 b. Evaluate - dx x 2 1 1 . c. Evaluate dx x x - 1 d. dx x - 2 1 2 1 3 e. ( 29 dx x x 4 3 2 5 + f. dx x x 3 cos sin 2 . Set up, but do not evaluate , the limit to find the area of the region bounded by 2 25 ) ( x x f - = and the x- axis between x = -1 and x = 3. The limit must be in the form where it is ready to be evaluated. 3. a. Evaluate ϑ ϑ ϑ π d - 2 0 2 3 cos 1 sin b. Find dx dy for ( 29 x y 3 sinh ln = 4. Evaluate = + n i n n n i 1 2 2 1 lim , given n n i = = 1 1 , 2 ) 1 ( 1 + = = n n i n i , ( 29 ( 29 6 1 2 1 1 2 + + = = n n n i n i 5. Evaluate + + dx x x 1 5 2 2 2 6. An object has a constant acceleration of 12 feet per second squared, an initial velocity of 17 feet per second, and a position of 40 feet after 1 second. Find the position function describing the motion of this object. You must show all your steps. 7. Evaluate dx x x - + - 2 4 3 5 8. a. Find the particular solution to

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Unformatted text preview: x C y cos-= and the initial condition 1 ) 3 / ( = y . b. Determine whether the function 3 2 2 3 4 2 ) , ( y xy y x x y x f-+-= is homogeneous, and, if so, determine its degree. 9. a. A radioactive element has a half-life of 50 days. What percentage of the original sample is left after 60 days? Round your answer to the nearest hundredth of a percent. b. All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is 1 cm? 10. a. Find the general solution to the first order differential equation: 2 ' = + y xy b. Find the general solution: ) ( 2 2 = + + dy xy dx y x 11. Evaluate: a. dt t t dx d x ) 2 3 ( 2 2 + ∫ b. dx x e e ∫-2 1 5...
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