Evaluate `underset (xrarr0)lim(xsecx)` ?

Prove that underset(xrarr0)lim(sinx)/x=1 , where x measured in radians , Also evaluate underset(xrarr0)lim(sin4x)/x ?

Evaluate underset(xrarr3)lim[x(x+1)] ?

Evaluate underset(xrarr0)lim((1-cosx)/(x)) ?

Prove that underset (x rarr 0) lim (sin x)/x=1 ,where x is in radian and hence evaluate: underset(x rarr 0)lim (sin 4x)/(sin 2x) .

Evaluate underset(xrarr0)lim(x^(3)-64)/(x-4) ?

Evaluate underset(xrarr0)lim ((x+1)^(2)-1)/(x) ?

Evaluate underset(xrarr0)lim[cosx/(pi-x)] ?

Evaluate underset (xrarr1)lim[(x^(2)+1)/(x+100)] ?

Evaluate : underset (x rarr 0)lim (3x-tan 4x)/(x+sin x) .

Evaluate: underset( x rarr 0)lim (ax+xcos x)/(b sin x) .