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Unformatted text preview: Integral Calculus Winter 2010-2011 Take-Home Quiz 1 Find the differential dy . 1. y = x (1- cos x ) 2. y = √ 36- x 2 3. Use differentials to approximate the value of the expression. 3 √ 63 Find the indefinite integral and check the result by differentiation 4. Z x 2- 3 x + 4 x 4 dx 5. Z 4 x 4 + sin x dx 6. Z (5cos x- 2sec 2 x ) dx 7. Solve the differential equation f ( x ) = 6 x 2- cos x, f (0) = 1 8. Find the particular solution of the differential equation f ( x ) =- 2 x whose graph passes through the point (- 1 , 1). 9. Find the particular solution of the differential equation f 00 ( x ) = 6( x- 1) whose graph passes through the point (2 , 1) and is tangent to the line 3 x- y- 5 = 0 at that point. 10. A ball is thrown vertically from a height of 5 feet with initial velocity of 50 feet per second. How high will the ball go? (Use a ( t ) =- 32 feet per second per second as the acceleration due to gravity. Neglect air resistance.) 11. The rate of growth dP/dt of a population of bacteria is proportional to the cube root of...
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This note was uploaded on 05/15/2011 for the course HIST 101 taught by Professor Mr.beckler during the Spring '11 term at Alabama State University.
- Spring '11