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For `xgt0, lim_(xto0) {(sinx)^(1//x)+((1)/(x))^sinx}`, is

Answer» `lim_(x->o^+)(sinx)^(1/x)+(1/x)^(sinx)`
let`L=lim_(x->0^+)(1/x)^sinx`
`lnL=lim_(x->0^+)sinx ln(1/x)`
`=lim_(x->0)ln(1/x)/(cosecx)`
LH hospital
`lnL=(x(1/x^2))/cot^2x=1/(xcot^2x)=tan^2x/x`
`lim_(x->0^+)tanx/x*tanx=0`
`lnL=0`
`L=e^0=1`


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