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

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Answer 1 · 2017-12-01T11:49:03

Undefined.

as #x->0^+# #color(white)(88)a^x->1#

as #x->0^-# #color(white)(88)a^x->1#

as #x->0^+# #color(white)(88)a^x/x->oo#

as #x->0^-# #color(white)(88)a^x/x->-oo#

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

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

#:.#

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