How do you find #lim sin(2x)/ln(x+1)# as #x->0# using l'Hospital's Rule?
Notice that attempting to evaluate the limit as
This is in a valid indeterminate form for l'Hopital's rule (the only two valid forms are
When one of these indeterminate forms is present, l'Hopital's rule states that:
So, we can take the numerator and denominator separately, as per l'Hopital's rule: