Question

Number 41

39. If the function f is defined by
0 if xis rational
f(x)
=
if x is irrational
prove that lim,o f(x) does not exist.
40. By comparing Definitions 2, 3, and 4, prove Thee
41. How close to -3 do we have to take x so that
1
> 10,000
(x+3)'
1
42. Prove, using Definition 6, that lim(x+3)
3. Prove that lim Inx =
-co

Image Transcription

39. If the function f is defined by 0 if xis rational f(x) = if x is irrational prove that lim,o f(x) does not exist. 40. By comparing Definitions 2, 3, and 4, prove Thee 41. How close to -3 do we have to take x so that 1 > 10,000 (x+3)' 1 42. Prove, using Definition 6, that lim(x+3) 3. Prove that lim Inx = -co

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