Evaluate the limits using the expansion formula of functions `("lim")_(xvec0){(sinx-x+(x^3)/6)/(x^5)}`

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)(e^(h-1-x))/(x^(2))

The value of lim_(xrarr0) (sinx-x+(x^3)/(6))/(x^5) , is

Evaluate lim_(xto0) (sinx-x)/(x^(3)).

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

Evaluate: (lim)_(xvec 0)(log(5+x)-log(5-x))/(x)

Find the following limit using expansion lim_(x rarr0)((ln(1+x)^(1+x))/(x^(2))-(1)/(x))

Column I ([.] denotes the greatest integer function), Column II ""("lim")_(xvec0)([100(sinx)/x]+[100(tanx)/x]) , p. 198 ("lim")_(xvec0)([100 x/(sinx)]+[100(tanx)/x]) , q. 199 ("lim")_(xvec0)([100(sin^(-1)x)/x]+[100(tan^(-1)x)/x]) , r. 200 ("lim")_(xvec0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x]) , s. 201

Evaluate of the following limit: (lim)_(x->0)(x-sinx)/(x^3)

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