  # 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

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Number 41 help_outlineImage Transcriptionclose39. 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 fullscreen
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Step 1

The inequality is given as

Step 2

The corresponding equation is

Step 3

Solve the equation and obtain the va...

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### Calculus 