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Math manipulation

  • Thread starter sparkle123
  • Start date
  • #1
175
0
Why does
86072215.png

when l approaches infinity?
This would mean that
ef174ec5.png
but I don't understand why that would be true.
Thanks!!
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
sqrt(1+r)=1+r/2-r^2/8+... That's the Taylor series expansion of sqrt(1+r). If r is small, then 1+r/2 is a good approximation. And as l->infinity then y^2/(l-x)^2 becomes very small. The sides aren't equal for any finite l. But the approximation becomes better and better as l->infinity.
 
  • #3
ehild
Homework Helper
15,427
1,825
Try it: Calculate the square root of 1+x with smaller and smaller x-values. For example, √1.2=1.095, √1.02=1.0099, √1.002=1.000999....

[itex]\sqrt{1+x} \approx 1+x/2[/itex]

ehild
 
  • #4
175
0
Thank you Dick and ehild! :)
 

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