(b)\( \int \frac{4x}{x^2+9} dx \)

3. Find the absolute maximum and minimum values of \( f(x) = \sqrt{4 - x^2} \), \( -2 \le x \le 1 \) .

4. Show that there is a real root of the equation between x3+x-1=0 and 1.

5. Find a power series for f(x)=ln x, centered at 1, and determine the interval of convergence.

(b) .

7. Show that is continuous, differentiable at x= 0 and find the value of f(0).

8. Find the area between and from x=0 to .

9. Evaluate the following limits

1. Water flows through a horizontal branching pipe as shown in Fig.1. Determine the pressure at section (3) (20％)

2. A piston having a cross-sectional area of 0.09 m2 is located in a cylinder containing water as shown in Fig. 2. An open U-tube manometer is connected to the cylinder as shown. For h1= 60 mm and h= 100mm, what is the applied force, P, acting on the piston? The weight of the piston is negligible. (20%)

3. The pressure drop, $\Delta p$, for incompressible turbulent flow in a horizontal round pipe of diameter $D$ can be written in functional form as \[ \Delta p = F(V, D, l, \epsilon, \mu, \rho) \] where $V$ is the average velocity, $l$ is the pipe length, $\epsilon$ is a measure of the roughness of the pipe wall, $\rho$ and $\mu$ are fluid density and viscosity, respectively. Find a non-dimensional relationship for $\Delta p$. (use $\rho, V, D$ as repeating variables) (20%)

115年 - 115 國立嘉義大學_碩士班(甲組)招生考試試題_應用數學系：微積分#143923

115年 - 115 國立嘉義大學_轉學生招生考試試題_理工學院：微積分#143894

115年 - 115 中央警察大學_碩士班入學考試試題_海洋科技組：微積分#139855

115年 - 115 中央警察大學_碩士班入學考試試題_消防科學研究所、交通管理研究所：微積分#139760

114年 - 114 國立嘉義大學_碩士班(甲組)招生考試試題_應用數學系：微積分#144160

114年 - 114 國立嘉義大學_轉學生招生考試試題_理工學院：微積分#143766

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題:微積分A#137897

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題：微積分B#137819

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137762

114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137761