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I came across this basic limits question

Lt

The part before '/'(the one separated by ][ is numerator and the one after that is denominator

The problem is if I substitute standard limits :

(Lt

Lt

Lt

The expression will simplify to

Lt

=Lt

Which is not defined

But if I had only put Lt

So why didn't I get the right answer using standard limits.

Regards

Lt

_{x->0}[(ln(1+X)-sin(X)+X^{2}/2]/[Xtan(X)Sin(X)]The part before '/'(the one separated by ][ is numerator and the one after that is denominator

The problem is if I substitute standard limits :

(Lt

_{x->0}tan(X)/x=1Lt

_{x->0}sin(X)/X=1Lt

_{x->0}ln(1+X)/X=1)The expression will simplify to

Lt

_{x->0}[X^{2}/2]/[X]^{3}=Lt

_{x->0}1/2XWhich is not defined

But if I had only put Lt

_{x->0}sin(X)=X and Lt_{x->0}tan(X)=X in the denominator, the denominator would become [X]^{3}and used polynomial expansion of ln(1+X) and sin(X) in numerator, the coefficient of [X]^{3}in the numerator would have been the answer (as smaller power terms cancel out and larger ones tend to 0) which here is 1/2, the correct answer.So why didn't I get the right answer using standard limits.

Regards

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