Answer to Question #21186 in Differential Equations for

Question

limits as x approaches -infinity (e^(2x)+e^x)/(ae^(2x)-e^x)

Answer 1

lim[ (e^(2x)+e^x)/(ae^(2x)-e^x) ]= here we divide all expression with e^{2x} =& lim[(1+e^{-x})/(a-e^{-x})] = here we are taking limit for every term in the numerator and denominator, and using the fact the e^(x) goes to 0 when x goes to -infinity = (1+0)/(a+0) = 1/a