If the value of `lim_(x rarr oo)(root(3)(x^(3)+x^(2))-root(3)(x^(3)-x^(2)))` can be expressed as `((a)/(b))` (where `a, b in N` and a & b are relatively prime numbers) then (a + b) is

The value of lim_(xtooo) (root(3)(x^(3)+2x^(2))-sqrt(x^(2)+x)) is

lim_(xrarroo) root3(x)(root3((x+1)^(2))-root3((x-1)^(2)))=

The value of lim_(xrarr oo) (3sqrt(x^3+x^2)-3sqrt(x^3-x^2)) , is

The value of lim_(xrarr1) (root(13)x-root7x)/(root5x-root3x) is

The real value of x satisfying ""^(3)sqrt(20x +^(3)sqrt(20x+13))=13 can be expressed as a/b where a and b are relatively prime positive integers. Find the value of b ?

lim_(xrarr oo) {3sqrt((x+a)(x+b)(x+c))-x}=

If range of f (x)= ((ln x) (ln x ^(2))+ln x ^(3)+3)/(ln ^(2) x+ln x ^(2)+2) can be expressed as [ (a)/(b),(c )/(d)] where a,b,c and d are prime numbers (not nacessarily distinct) then find the value of ((a+b+c+d))/(2).

Prove that Lim_(x to 0) (root3((1+x))-root3((1-x)))/x = 2/3

if a N= {a x:x in N} and b N cap c N = dN , where b,c in N are relatively prime , then

Evaluate lim_(xto2) (sqrt((x+7))-3sqrt((2x-3)))/(root(3)((x+6))-2root(3)((3x-5))).