ksaimouli
  • ksaimouli
limit
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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ksaimouli
  • ksaimouli
\[(1/x- 1/5)/(x-5)\]
ksaimouli
  • ksaimouli
as x-> 5
amistre64
  • amistre64
what are the degrees of the top and bottom?

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More answers

ksaimouli
  • ksaimouli
1
amistre64
  • amistre64
-1 and 1 do you recall your rules for degrees?
ksaimouli
  • ksaimouli
What do you mean by degree? You mean power of x?
amistre64
  • amistre64
yes
amistre64
  • amistre64
might only work for proper polynomilas tho simplify by multiplying top and bottom by 5x
ksaimouli
  • ksaimouli
5-x/(5x^2-25x)
amistre64
  • amistre64
(5-x)/(5x(x-5)) -(x-5)/(5x(x-5)) -/(5x)
amistre64
  • amistre64
-1/(5x)
ksaimouli
  • ksaimouli
-1/25, got you
ksaimouli
  • ksaimouli
or we could use L'hospitals rule right?
anonymous
  • anonymous
Or just the definition of the derivative.
amistre64
  • amistre64
the fractiony top part tends to play havok with derivatives, but its worth a shot if you are allowed to use it
amistre64
  • amistre64
1/x derives to -1/x^2 ... and the limit thing is usually x to 0 tho
ksaimouli
  • ksaimouli
By looking at it, how did you come up to multiply by 5x?
amistre64
  • amistre64
/x and /5 have 5x as a common denomto clear the fractions
ksaimouli
  • ksaimouli
Got you! thanks
amistre64
  • amistre64
lhop has no issues with this
amistre64
  • amistre64
good luck
anonymous
  • anonymous
For \(h\to0\), where \(h\) represents the difference between two values of the independent variable. You can make a small modification to that definition to arrive at the derivative at a point: \[f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}~~\implies~~f'(c)=\lim_{x\to c}\frac{f(x)-f(c)}{x-c}\]

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