Question #6c4e4

1 Answer
Dec 23, 2017

Lim_(xrarr1)(sinx-sin(1/x))/(e^x-e^(1/x))~~0,1987

Explanation:

Lim_(xrarr1)(sinx-sin(1/x))/(e^x-e^(1/x))=0/0

Using L'Hopitals rule:

Lim_(xrarr1)(sinx-sin(x^-1))/(e^x-e^(x^-1))

Lim_(xrarr1)(cosx-cos(x^-1)*-1*x^-2)/(e^x-e^(x^-1)*-1*x^-2)

Lim_(xrarr1)(cosx+(cos(x^-1))/x^2)/(e^x+(e^(x^-1))/x^2)

(cos1+cos1/1^2)/(e+e/1^2)=(cancel2cos1)/(cancel2e)=cos1/e~~0,1987