Evaluate the following limit: `lim_(x->0)(x^2+1-cos x)/(xsinx)`

Explanation

`lim_(x->0)(x^2+1-cos x)/(xsinx)`

`=lim_(x->0)(x^2+2sin^2(x/2) )/(xsinx)`

`=lim_(x->0) (x^2(1+2((sin(x/2))/(x/2))^2))/(xsinx)`

`=lim_(x->0) (1+2((sin(x/2))/(x/2))^2 xx 1/4)/((sinx)/x)`

`=(1+2lim_(x to 0)((sin(x/2))/(x/2))^2 xx 1/4)/(lim_(x to 0)(sinx)/x)`

`=1+1/2`

`=3/2`