`underset(xrarroo)(lim)(sum_(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))=`

underset(xrarroo)(lim)(sinx/x)

If underset(xrarroo)"lim"((1+x)^(10)+(x+2)^(10)+....+(x+100)^(10))/(x^(10)+10^(10)) =K^(2) , then the value of K will be -

underset(xrarr1)(lim)(2/(1-x^2)+1/(x-1))

underset(xrarr0)"lim"(a^(2x)-1)/(x) =

underset(xrarr1)"lim"(x-1)/(sqrt(x)-1)= ?

underset(x rarr 1)lim (x^(3)-1)/(x^(2)-1) =

Prove : underset(xrarroo)"lim"(cosx)/(x)=0

Prove : underset(xrarroo)"lim"(sinx)/(x)=0

underset(xrarroo)"lim"[(x)/(x-2)-(4)/(x^(2)-2x)] is -

Statement -I : underset(xrarroo)"lim"(1^(2)/(x^(3))+(2^(2))/(x^(3))+3^(2)/(x^(3))+......+x^(2)/(x^(3)))= underset(xrarroo)"lim"(1^(2))/(x^(3))+underset(xrarroo)"lim"(2^(2))/(x^(3))+....+underset(xrarroo)"lim"(x^(2))/(x^(3))=0 Statement - II : underset(xrarra)"lim"{f_(1)(x)+f_(2)(x)+....+f_(n)(x)}=underset(xrarra)"lim"f_(1)(x)+underset(xrarra)"lim"f_(2)(x)+...+underset(xrarra)"lim"f_(n)(x)"