Question

詩人

請問37、43題怎麼證明（需要用delta和epsilon）

d
ind36. Prove that lim-
1. 1
-=
x-2 X
2°
37. Prove that lim√√√√a if a > 0.
xa
=
x-a
Hint: Use | √x - √a |- 1x = 4/4]
=
√x +
√a
38. If H is the Heaviside function defined in Example 6 in Sec-
tion 2.2, prove, using Definition 2, that lim,-0 H(t) does not
exist. [Hint: Use an indirect proof as follows. Suppose that the
limit is L. Take & in the definition of a limit and try to
=
arrive at a contradiction.]
39. If the function f is defined by
f(x) =
So if x is rational
=
1 if x is irrational
prove that lim x->0 f(x) does not exist.
40. By comparing Definitions 2, 3, and 4, prove Theorem 1 in
Section 2.3.202
41. How close to -3 do we have to take x so that
1
> 10,000
(x+3)4
1
42. Prove, using Definition 6, that lim
80.
x-3 (x+3)4
5
43. Prove that lim
-80.
x-1 (x + 1)³

Answer 1

林明治

。