109年 - 109 元智大學轉學生招生考試試題_工業工程與管理學系：微積分#114203

科目：研究所、轉學考(插大)-微積分 | 年份：109年 | 選擇題數：0 | 申論題數：14

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (14)

a. (2 points)cosh^-1x=1/cosh(x)

b. (2 points) If a function is invertible then it is one-to-one function.

c. (2 points) Substitution rule is an inverse process of chain rule.

a. (2 points) How is the number e defined?

b. (2 points) How to transform general exponential function a^x to a natural exponential function?

a.

b.

c. ∫ 11^x｜2x cosh(x)dx

d. ∫ x cosh(1+4x²)sinh(1+4x²)dx

a. Find the area bounded by x=1+y² and y=x-4.

b. Find the volume of the solid obtained by rotating the region bound by x = 1+y² ,y=x-4 about the y-axis.

3. (10 points) Find the radius of convergence and interval of convergence of

4. (10 points) Please find the Gradient and Hessian for the function f(x)=x³y+e^2xy+2y².

5. (10 points) Find the Taylor series for