How to solve lim (lnx+3)/e^2x as x approaches to positive infinity? How to solve lim (lnx+3)/e^2x as x approaches to positive infinity? @Mathematics

Question

unklerhaukus · Answer

as x approaches infinity the ratio becomes infinity / infinity.
this is not a solution, use L'Hopitals rule; differentiate the denominator and the numerator then try again, repeat if necessary

anonymous · Answer

can you write the solution for differentiating?

unklerhaukus · Answer

$${\delta \over \delta x} (lnx+3) = 1/x$$

$$ { \delta \over \delta x} (e^{2x}) = 2e^{2x} $$

unklerhaukus · Answer

so your ratio becomes $$ {1/x \over 2e^{2x}}$$
take the limit as x approaches infinity,
 the only solution is 1/infinity which equals zero