What is the limit of (a^x)/x as x approaches 0? Can this limit be calculated using LH Rule?

1 Answer
Dec 1, 2017

Undefined.

Explanation:

as x->0^+x0+ color(white)(88)a^x->188ax1

as x->0^-x0 color(white)(88)a^x->188ax1

as x->0^+x0+ color(white)(88)a^x/x->oo88axx

as x->0^-x0 color(white)(88)a^x/x->-oo88axx

lim_(x->0^+)(a^x/x)=oo

lim_(x->0^-)(a^x/x)=-oo

:.

lim_(x->0)(a^x/x)=undefined