106年 - 106 國立清華大學碩士班考試入學試題_科技管理研究所/乙組:微積分#110853

2. Evaluate

3. A function f is defined by

 Find the maximum value of f.

4. Find the solution of the differential equation

 that satisfes the initial condition y (1) = 0.

5. If f is concave upward on [a,b], show that

6. If a_o + a₁ + a₂ +...+ = 0, show that

7. Find the minimum distance from the origin in to the surface z = 6xy + 7.

8. Evaluate

where R is the plane region determined by the conditions x² + y²≤1 and : x+y≥1.