`("lim")_(xvec0)(sinx^n)/((sinx)^m),(m

If m , n in N ,("lim")_(xvec0)(sinx^m)/((sinx)^m)i s 1,ifn=m (b) 0,ifn > m oo,ifn

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

("lim")_(xvec0)(x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then, (a) a+c (b) 1 (c) -1 (d) none of these

("lim")_(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c) 1 (d) -1

("lim")_(xvec0)[(sin(sgn(x)))/((sgn(x)))], where [dot] denotes the greatest integer function, is equal to (a)0 (b) 1 (c) -1 (d) does not exist

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

("lim")_(xvec0)(5sinx-7sin2x+3sin3x)/(x^2sinx)

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)(1-cos2x)/(x^2)

Evaluate: ("lim")_(xvec0)(1-cosm x)/(1-cosn x)