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Unformatted text preview: . Find the dimensions of the box that would minimize the cost. 6. Find the most general antiderivatives of the following functions. 2 20 x5
f ( x) 4sec 2 x sin x f ( x) x 2 a)
b) 7. Find the particular antiderivative of the following. a) f ( x ) e , F (0) 2 x 8. b) g ( x ) x 3x 23 , G (1) 3 A lighthouse is located on an island 5 miles from the nearest point P on a straight shoreline and its light makes 6 revolutions per minute. How fast is the beam of light moving along the shoreline when it is 2 miles from P ? (Hint: 1 revolution = 2 radians) 9. Use differentials to approximate sin(31) . (Hint: Be sure to convert to radians.) 10. Verify the following integrals give the indicated result. a.
c. dx
x 10 x x x 2
2 1 2 10 x x 2 b. C 5x d. dx ln x 1 ln x 1 C (e 2e
x e e
x x e e
x dx 2 x x C 2 e 1
x 1) 2 dx e 1
x C 11. Estimate the area under the curve f ( x ) x 3 x on the interval [1,9] using 4 rectangles and right Riemann Sums. 12. Find the following limits. 1
2
5
b) lim e x x x c) lim 4 ln x...
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This note was uploaded on 02/24/2014 for the course MATH 1151 taught by Professor Daniel during the Fall '12 term at Ohio State.
 Fall '12
 daniel
 Math

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