39. If the function f is defined by0 if xis rationalf(x)=if x is irrationalprove that lim,o f(x) does not exist.40. By comparing Definitions 2, 3, and 4, prove Thee41. How close to -3 do we have to take x so that1> 10,000(x+3)'142. Prove, using Definition 6, that lim(x+3)3. Prove that lim Inx =-co

Question
Asked Sep 15, 2019

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
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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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Step 1

The inequality is given as

1
10,000
x+3)
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1 10,000 x+3)

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Step 2

The corresponding equation is  

1
= 10,000
(x+3)
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1 = 10,000 (x+3)

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Step 3

Solve the equation and obtain the va...

1
= 10,000
(x+3)
1
(x +3)
10,000
1
- (x+3)
(10)
1
x3 =
10
x = -2.9
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1 = 10,000 (x+3) 1 (x +3) 10,000 1 - (x+3) (10) 1 x3 = 10 x = -2.9

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Math

Calculus