Saturday, 24 September 2016

calculus - limxtoinftyfracex/22x



How do i know what is the limit :



lim



Because with l'hopital it is imposible to say, as the nth derivatives of both {e^{x/2}} and {2^x} are always infinity...
I could use a hint that helps me think this through


Answer






\large\frac{e^{x/2}}{2^x}=\frac{e^{x/2}}{e^{x\ln(2)}}=e^{x\left[\frac12-\ln(2)\right]}\to\ ...


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