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

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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 ________

5. The integral In x dx =_______

6. The integralx =______

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.

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