This is how I would evaluate limx→∞x+sinxx+2sinx
=limx→∞x(1+sinxx)x(1+2⋅sinxx)
=1+01+2⋅0=1
But now applying L'hopitals Rule, I get
limx→∞1+cosx1+2cosx
Since cosx just oscillates between [−1,1] I think we can conclude the limit doesn't exist.
What is going on here?
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