Prove that `underset(xrarr0)limsinx/x=1` ?

Prove that underset(xrarr0)lim(sinx/x=1) ?

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

Prove that underset(xrarr0)lim (a^x-1)/x= log a .

underset (xrarr0)lim x^(x)

Prove that, underset(xrarr0)lim (logcosx)/sin^2x = -1/2

Prove that: underset(xrarr0)lim [1+3x]^((x+3)/x = e^9

Prove that underset(xrarr0)"lim"(3x+|x|)/(7x-5|x|) does not exist .

Evaluate: underset(xrarr0)limx^x

underset(xrarr0)lim (sin4x)/(sin2x) is:

Prove : underset(xrarr0)"lim"(tanx-sinx)/(1-cosx)=0