Show : `underset(xrarr2)"lim"((1+x)^(n)-3^(n))/(x-2)=n.3^(n-1)`

Starting from underset(xrarra)"lim"(x^(n)-a^(n))/(x-a)=na^(n-1)" deduce that ," underset(xrarr0)"lim"((1+x)^(n)-1)/(x)=n.

Show that underset(xrarr2)"lim"(x^(2)-3x+5)=3 .

Show that underset(xrarr-2)"lim"(x^(3)-5x+3)/(x^(2)+1)=1

show that underset(xrarr-2)"lim"sqrt(x^(3)+3x^(2)-x+3)=3

underset(xrarr-(1)/(2))"lim"(2x^(2)-3x+1)/(2x-1)= ?

Show that underset(xrarr1)"lim"(1)/(x-1)^(2)=+oo .

Evaluate : underset(xrarr2)"lim"(x^(2)-3x+2)/(x^(3)-5x+2) .

Evaluate : underset(xrarr1)"lim "(x^(2)-3x+2)/(x^(2)-4x+3)

underset(xrarr1)"lim"(x+x^(2)+x^(3)+.....+x^(n)-n)/(x-1) =

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)"