Help me to calculate this limit
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Solved by rtournem,
Hello!
You can factor in order to remove the (1-1) problem using the "identités remarquables" (I'm french ^^):
(e^(3x) - 1) / (e^(4x) - 1)=A/B
A=(e^x)^3 - 1^3)=(e^x-1)(e^(2x)+e^x+1)
B=((e^(2x))^2 - 1^2)=(e^(2x)-1)(e^(2x)+1)=(e^(x)-1)(e^x+1)(e^(2x)+1)
You've done the hardest. Now just simplify (e^x-1):
A/B=(e^(2x)+e^x+1)/(e^x+1)(e^(2x)+1) --- x=0 ---> 3/4
Tadammmmm!
If you hate to have to "see" the solution just use the "développement limité" around 0 of f(x) (In your case f(x)=e^(4x) and f(x)=e^(3x))
https://fr.wikipedia.org/wiki/Développement_limité
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