Limit diverges or converges

  • Thread starter graycolor
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  • #1
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integral 2/(x-6)^2 respects to x from 0 to 8. Shouldn't the answer to this be converges and is =-4/3. The true answer to this is it diverges towards infinity... can someone please explain.
 

Answers and Replies

  • #2
statdad
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Two things to consider:

1. isn't there a number between [tex] 0 [/tex] and [tex] 8 [/tex] that could cause a problem?

2. The integrand [tex] 2/{(x-6)^2}[/tex] is positive throughout the interval of integration,
so how could the integral be negative?
 
  • #3
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I think I've found the problem there should be an asymptote when x=6. My teacher never taught me to look for these.
 
  • #4
statdad
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Whether you are graphing, integrating, differentiating, or simply contemplating the function and its domain for their inherent beauty :rofl: you should always look for the possible existence, and influence of, an asymptote for rational functions.
 

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