Solve `lim_(x->0) xsin(1/x)`

solve lim_(x->0) (x^2-sin^2x)/(xsinx)

solve lim_(x->0) (x^2+1-cosx)/(xsinx)

Evaluate the following: (lim)_(x->0^+)xsin1//x

lim_(x->0)(1/x)^(1-cosx)

lim_(x->0) (x^3-3x+1)/(x-1)

lim_(x->0) (x^2-3x+1)/(x-1)

What is the value of lim_(x to 0) (xsin5x)/(sin^(2)4x)

Solve (i) lim_(xto1) sin x (ii) lim_(xto0^(+))[(sinx)/x] (iii) lim_(xto0^(-))[(sinx)/x] (where [.] denotes greatest integer function)

To show lim_( x to 0) "x sin" 1/x =0 .

Evaluate "lim_(x rarr0)x tan(1/x)