Question 1204215


given:

{{{lim(x->-infinity,(e^(ln(ax))*tan((2a)/x)))= 8}}}

manipulate left side

{{{lim(x->-infinity,(e^(ln(ax))*tan((2a)/x)))}}}.........since {{{e^(ln(ax))=ax}}}, we have


{{{lim(x->-infinity,(ax* tan((2a)/x)))}}}

then

{{{lim(x->-infinity, ax* tan((2a)/x))=  2a^2}}}


equal it to right side


 {{{2a^2=8}}}

 {{{a^2=4}}}

{{{a=2}}} =>solution

{{{a=-2}}} =>not a solution

check:

{{{lim(x->-infinity,(e^(ln(2x))*tan((2*2)/x)))= 8}}}
{{{8= 8}}}

{{{lim(x->infinity,(e^(ln(2x))*tan((2*2)/x)))= 8}}}
{{{8= 8}}}