Evaluate: `("lim")_(nvec0)(1-"cos"(1-cosx)dot)/(x^4)`

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

Evaluate ("lim")_(xvec0) (sinx-2)/(cosx-1)

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)

lim_(xto0)(1-cos(1-cosx))/(x^(4)) is

Evaluate lim_(xto0) (1-cos(1-cosx))/(x^(4)).

Evaluate: ("lim")_(xvecpi/4)(sqrt(2)cosx-1)/(cotx-1)

Evaluate: ("lim")_(xrarr0) (sin[cosx])/(1+[cosx])([dot] denotes the greatest integer function).

Evaluate: ("lim")_(nvec1)("sin"{x})/({x}) if exists, where {x} is the fractional part of xdot

("lim")_(xvec0)("cos"(tanx)-cosx)/(x^4)i se q u a lto 1/6 (b) -1/3 (c) 1/2 (d) 1

Evaluate lim_(xto0)(1-cos4x)/(x^(2))