100年 - 100 國立中興大學_轉學考招生試題：A組聯招群：微積分#110064

1. By the limit definition, _______

2. The mathematical constant e = 2.71828... is sometimes called Euler's number, and can be defined as a limit of _______

3. The Maclaurin's series for is ________

4. In the Composite Limit Theorem, , the least required sufficient conditions are that _______

5. The integral  In x dx =_______

6. The integralx =______

7.=_______

8. The temperature on the surface of a metal plate is T(x, y) =. The direction of the greatest increase in heat from point (3, 4) is_______； The rate of increase in the direction from point (3, 4) to point (6, 8) is _______.

9. If a curve is given by , where 0≤ t ≤4π and b is a constant, the length of the curve is ________

1. Find the average of the function f(x) = x sin x between x =0 and x=π.

2. The eror functon erf(x) is defined as erf(x)=. Use this formula to find the integral .

3.For dx dy ,(1)sketch the region of integration； (2) switch the order of integration and evaluate the integral.

4. Evaluate the line integral ，where C. line segment from (1, 1) to (Hint:)

5.Find the area of the region Iying between the inner and outer loops of the limacon r(θ) =1-2sinθ.