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

Evaluate: ("lim")_(xvec2)(x-2)/((log)_a(x-1))

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

Evaluate: ("lim")_(xrarr0)(sinx^0)/x

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

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")_(xvec0)(sin^(-1)x-tan^(-1)x)/(x^3)

Let p_n=a^(P_(n-1))-1,AAn=2,3, ,a n dl e tP_1=a^x-1, where a in R^+dot Then evaluate ("lim")_(xvec0)(P_n)/x

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

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

Evaluate the limit: ("lim")_(xvec0)(sina x)/(sinb x)