所屬科目：研究所、轉學考(插大)-微積分
1.4 True or False: The function f(x) is differentiable at x =.
1.5 Let n be a strictly positive integer. Find out f(x)dx, if exists； if the integral does not exist, explain why.
1.6 True or False: Given any a,b ∈ such that a ＜ b, if there exists a function g(x) such that ,then f(x) = g(x)for all x ∈ [a, b].
2.1 If |x(x-2)|dx = 0,then a =________.
2.2 =________.
2.3 =________
2.4 If f(x) = sin[sin(sinx)],then =________ at x =0.
2.5 If f(x)= for x ＞ 0, then = ________, and =________.
2.8 Suppose that the three variables x,y, and a satisfy x3+y2+z = 3 and x•y2•z3 = 1. Then =________and =________ at the point (x,y,z) = (1,1,1).
3.1 f(x) =,where 0 ≤ x ≤ 10.
3.2 f(x,y) = x • sin y,where x,y ∈ R.
4. Consider the infinite series , where a ＞ 0. Find the necessary and sufficient condition of a such that the series is convergent, or argue that no such condition exists.
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f(x)dx, if exists； if the integral does not exist, explain why.
such that a ＜ b, if there exists a function g(x) such that 
,then f(x) = g(x)for all x ∈ [a, b].
|x(x-2)|dx = 0,then a =________.
=________.
=________
=________ at x =0.
for x ＞ 0, then 
= ________, and 
=________.
=________and 
=________ at the point (x,y,z) = (1,1,1).
,where 0 ≤ x ≤ 10.
, where a ＞ 0. Find the necessary and sufficient condition of a such that the series is convergent, or argue that no such condition exists.