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  #1  
Old 05-25-2018, 12:07 PM
ericp ericp is offline
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Default What is the limit?

Anyone know how to evaluate this limit?

(10,000 / (x+10,000))^2
Y = divided by
(x goes to infinity) (20,000 / (20,000 +x^2)

The answer is 10,000^2 / 20,000. I don't get that answer. The solution did not show method.

Switching terms around I have
[10,000^2/20,000] * [(x+10,000)^2 /(20,000 + x^2)]. If the right side was 0/0 i would take the derivative of numerator and denominator and try again but I don't think that works for infinity divided by infinity.

Anyone out there know why the right side end up being one?
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Old 05-25-2018, 03:16 PM
SIGUS SIGUS is offline
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0/0 and infinity/infinity are both indeterminate limit forms so the l'hopital's rule can be applied in both situations
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Old 05-25-2018, 05:33 PM
Abraham Weishaus Abraham Weishaus is offline
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Quote:
Originally Posted by ericp View Post
Anyone know how to evaluate this limit?

(10,000 / (x+10,000))^2
Y = divided by
(x goes to infinity) (20,000 / (20,000 +x^2)

The answer is 10,000^2 / 20,000. I don't get that answer. The solution did not show method.

Switching terms around I have
[10,000^2/20,000] * [(x+10,000)^2 /(20,000 + x^2)]. If the right side was 0/0 i would take the derivative of numerator and denominator and try again but I don't think that works for infinity divided by infinity.

Anyone out there know why the right side end up being one?
You can take derivatives twice and use L'Hospital. Probably simpler is noticing that the numerator and denominator are both quadratic polynomials, and the x^2 term in each dominates, so the limit is the coefficient of x^2 in numerator divided by coefficient of x^2 in denominator.
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  #4  
Old 05-30-2018, 12:07 PM
ericp ericp is offline
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Thanks for responses. I did not realize that both were indeterminate forms and forgot that the highest term in numerator and denominator dominate for limits.
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