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

lim_(xrarr0) (sinx^n)/((sinx)^m), (mltn) is equal to

Which of the following limits tends to unity? (a) ("lim")_(xvec0)sin(tanx)/(sinx) (b) ("lim")_(xvecpi/2)sin(cosx)/(cosx) ("lim")_(xvec0)"sin"(e^x-1)/x (d) ("lim")_(xvec0)(sqrt(1+x)-sqrt(1-x))/x

If m,n inN,lim_(xto0) (sinx^(n))/((sinx)^(m)) is

lim_(x->0)|sinx|/x

lim_(xrarr0) (x^(2)-x)/(sinx)

Evaluate the following (10-17) limits : lim_(x to 0)(sin3x-sinx)/(sinx)

Column I ([.] denotes the greatest integer function), Column II ""("lim")_(xvec0)([100(sinx)/x]+[100(tanx)/x]) , p. 198 ("lim")_(xvec0)([100 x/(sinx)]+[100(tanx)/x]) , q. 199 ("lim")_(xvec0)([100(sin^(-1)x)/x]+[100(tan^(-1)x)/x]) , r. 200 ("lim")_(xvec0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x]) , s. 201

If lim_(xtoa)f(x)=1 and lim_(xtoa)g(x)=oo then lim_(xtoa){f(x)}^(g(x))=e^(lim_(xtoa)(f(x)-1)xg(x)) lim_(xto0)((sinx)/x)^((sinx)/(x-sinx)) is equal to

lim_(x to 0) (e^x-e^sinx)/(x-sinx)

lim_(xrarr0) (sinx)/(x)= ?