meters from the bottom of the triangle with height dxarea 2xdx. The depth of this slice is D= 3 - x. The pressure on this slice is P= ρgD= ρg(3 - The force acting on this slice is dF= PA= 2ρgx(3 – x)dx. The total force acting on this slice is = 02(3)gxx dxρ-∫. 100,000. Then Twater level1 m4 m2 mxhas x). F25. Suppose the population of a culture of bacteria grows exponentially. At time t= 0, the population is 10,000, and the population reaches 30,000 at t= 2. At time Tthe population is =

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Chapter 9 / Exercise 36

**Mathematical Applications for the Management, Life, and Social Sciences**

Harshbarger

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MAT1322-3X Solution to Final Examination Summer 2014 3

6. SupposeEuler's method with step size h= 0.1 is used to estimate y(0.3), where y(t) is the solution to the initial-value problem y'= 2ty2-y2, y(0) = -1. Which one of the following values is closest to the result that you obtained?

-1.431.

0= -1.

n

-1

7. The sum of the series01

(F) 113.

8. Consider power series 0( 1)3-∑. Which one of the following statement is true?

(A) When -3 < x< 3, this series is absolutely convergent. When x≤-3 or x≥3, it is divergent. (B) When -3 < x< 3, this series is absolutely convergent. When x< -3 or x≥3, it is divergent. When x= -3, this series is convergent but not absolutely convergent.

MAT1322-3X Solution to Final Examination Summer 2014 4 (C) When-3 < x< 3, this series is absolutely convergent. When x≤-3 or x> 3, it is divergent. When x= 3, this series is convergent but not absolutely convergent. (D) When -3 < x< 3, this series is convergent but not absolutely convergent. When x≤-3 or ≥3, it is divergent. (E) When -3 < x< 3, this series is convergent but not absolutely convergent. When x< -3 or ≥3, it is divergent. When x= -3, it is absolutely convergent. (F) When -3 < x

x

x