Evaluate the limits using the expansion formula of functions `("lim")_(xvec0)(e^x-1-x)/(x^2)`

Evaluate the limits using the expansion formula of functions lim_(x rarr0)(sin x+log(1-x))/(x^(2))

Evaluate the limits using the expansion formula of functions lim_(x rarr0){(sin x-x+(x^(3))/(6))/(x^(5))}

Applying the L.Hospital rule , find the limits of the following functions : lim_(xto0) (e^(x)-e^(-x)-2x)/(x-sin x)

Applying the L.Hospital rule , find the limits of the following functions : lim_(xto0) (e^(ax)-e^(-2ax))/(ln(1+x))

Evaluate of the following limit: (lim)_(x->0)(e^x-1-x)/(x^2)

Applying the L.Hospital rule , find the limits of the following functions : lim_(xto0) (ln(1+x^(2)))/(cos3x-e^(-x))

Evaluate the following limits using sandwich theorem: lim_(x rarr oo)(log_(e)x)/(x)

Evaluate the limit: (lim)_(xvec 1)(sin(log x))/(log x)

Using the L .Hospital rule find limits of the following functions : lim_(x to oo) (e^(1//x^(2)-1))/(2"arc tan"x^(2)-pi)

If f(x)=x((e^(|x|+[x])-2)/(|x|+[x])) then (where [.] represents the greatest integer function) (lim)_(xvec0^+)f(x)=-1 b. (lim)_(xvec0^-)f(x)=0 c. (lim)_(xvec0^)f(x)=-1 d. (lim)_(xvec0^)f(x)=0