Evaluate: `("lim")_(nvec0)(2^x-1-x)/(x^2),` without using LHospitals rule and expansion f the series.

Evaluate: ("lim")_(xto0)(e^x-1-x)/(x^2), without using LHospitals rule and expansion f the series.

Evaluate: lim_(n rarr0)(2^(x)-1-x)/(x^(2)), without using LHospitals rule and expansion f the series.

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

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

Evaluate ("Lim")_(x->0)(2^x-1)/((1+x)^(1//2)-1) using Lhospitals Rule

Evaluate ("lim")_(x -> 0)(x-sinx)/(x^3)dot (Do not use either LHospitals rule or series expansion for sinxdot)dot Hence, evaluate ("lim")_(x -> 0)(sinx-xcosx+x^2cotx)/(x^5)

Evaluate ("Lim")_(x->0)[1/(x^2)-1/(sin^2x)] using LHospitals Rule or otherwise :

lim_(x->0)(1+sinx-cosx+ln(1-x))/(x*tan^2x) using LHospitals Rule

Evaluate ("Lim")_(x->0)(1+sinx-cosx+ln(1-x))/(x tan^2x) using LHospitals Rule or otherwise :