[討論] 微積分作業

[selient (假安靜)]

4.Suppose that g ia an increasing function on an interval [a,b] and g is
  continuous at every point on [a,b].Let-1g denote the inverse function
  of g when the domain of g is restricted to [a,b]. Suppose that
  g(a) < c < g(b).Then the following statement is true.

For every ε> 0, take ξto be the minimum of b - g-1(c), g-1(c) - a andε
,and take δto be the minimum of [g(g-1(c)+ξ) - c] and [c - g(g-1(c) - ξ)]
.Then

   ∣X - c｜<δ => ｜g-1(x) - g-1(c)｜<ε

  What does the above statement say about lim g-1(x)?
                                          x->c

5.Suppose that f(x)=x/sinx for x≠0 and f is continuous at 0.
  (a) What is f(0)?
  (b) Show that f is continuous at c for every c in (-∞,∞).
  (c) Find that lim f(sin-1(x)) using the Composition Limit Rule (p.73 in
                x->c
      the text) and the result from Problem 4.




God damn hard!


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