`lim_(x->oo)(3/x)[x/4]= p/q`find `p+q`

lim _(xtooo)3/x [(x)/(4)]=p/q where [.] denotes greatest integer function), then p+q (where p,q are relative prime) is:

Let f : R to R be a real function. The function f is double differentiable. If there exists ninN and p in R such that lim_(x to oo)x^(n)f(x)=p and there exists lim_(x to oo)x^(n+1)f(x) , then lim_(x to oo)x^(n+1)f'(x) is equal to

The value of lim_(x to1)(p/(1-x^p)-q/(1-x^q)),p ,q , in N , equal (a) (p+q)/2 (b) (p q)/2 (c) (p-q)/2 (d) sqrt(p/q)

Evaluate lim_(x to oo) (ax^(p) + bx^(p- 3) + c)/(a_(1)x^(q) + b_(1)x^(q-1) + C_(1)X^(q-3) + d_(1)) Where p gt 0, q gt 0 , a,b,c, a_(1), b_(1),C_(1),d_(1) are constants.

Evaluate : lim_(x to oo) ((x-3)/(x+3))^(x+3)

Let lim _( x to oo) n ^((1)/(2 )(1+(1 )/(n))). (1 ^(1) . 2 ^(2) . 3 ^(3)....n ^(n ))^((1)/(n ^(2)))=e^((-p)/(q)) where p and q are relative prime positive integers. Find the value of |p+q|.

Evaluate the following limits : Lim_(x to oo) ((x+1)(2x+3))/((x+2)(3x+4))

If p(x)=x^(5)+4x^(4)-3x^(2)+1 " and" g(x)=x^(2)+2 , then divide p(x) by g(x) and find quotient q(x) and remainder r(x).

Divide p(x) by g(x) and find the quotient q(x) and remainder r(x). p(x)=x^(4)+2x^(2)+3, g(x)=x^(2)+1

If p , r , s gt 0 then lim_(x rarr oo)((p^(1/x)+q^(1/x)+r^(1/x)+s^(1/x))/4)^(3x)