`underset(xrarroo)(1^(2)+2^(2)+3^(2)+...+x^(2))/(X^(3))`

lim_(xrarroo) (1^(2)+2^(2)+3^(2)+....+x^(2))/(4x+3)

lim_(xrarroo)((1^(4)+2^(4)+3^(4)+….+x^(4)))/(x^(2)(1^(2)+2^(2)+……+x^(2))) equals

Find underset( x rarr oo )("lim") ((1-2x)/((1+ 8x^(3))^(1//3))+2^(-x^(7)))

Evaluate the following limits and justify each step. underset(xrarr -2) ( "Lim") ( x^(3)+2x^(2) -1)/(5-3x)

Find the limits : (a) underset(x to oo)lim ((2x^(2)+3)/(2x^(2)+5))^(8x^(2)+3) (b) underset(x to 0)lim ((1+tan x)/(1+tan x))^(1//sin x) (c ) underset(x to 1)lim (1+sin pi x)^(cot pi x) (d) underset(x to a)lim ((sin x)/(sin a))^(1//(x-a)) (a ne kpi," with k integer")

underset x rarr2^(-)lim_(x rarr2^(-))[(x^(2))/(a)]^((1)/(|x-2|))=1 Then find the range of

lim_(xrarroo) (x^(3)+3x^(2)+6x+5)/(x^(3)+x+2)

Lim_(xrarroo)(x/(x+2))^x