Evaluate : `("lim")_(xvec2)(x^2-5x+6)/(x^2-4)`

Evaluate: ("lim")_(xvec-2^+) (x^2-1)/(2x+4)

Evaluate : ("lim")_(xvec1)(2/(1-x^2)+1/(x-1))

Evaluate: ("lim")_(xvec0)(1-cos2x)/(x^2)

Evaluate: ("lim")_(xvec0xvec0)(y^2+sinx)/(x^2+siny^2) where (x , y)vec(0,) along the curve x=y^2

Evaluate ("lim")_(xvec0)(x-sinx)/(x^3)dot (Do not use either LHospitals rule or series expansion for sinxdot)dot Hence, evaluate ("lim")_(nvec0)(sinx-x-xcosx+x^2cotx)/(x^5)

Evaluate : ("lim")_(xvec1)(x^2+x(log)_e x-(log)_e x-1)/((x^2-1)

Evaluate: ("lim")_(xvec0)(1+x)^(os e cx c)

Evaluate: ("lim")_(xvec0)(cot2x-cos e c2x)/x

Evaluate lim_(xto-1)(x^(2)-5x+6)/(x-1)

Evaluate: ("lim")_(xvec0)((1-3^x-4^x+12^x))/(sqrt((2cosx+7)-3))