lim_(x rarr oo)(3)/(x) [(x)/(4)] =(p)/(q) find p and q

Let P and Q be polynomials. Find Lim_(x->oo) (P(x))/(Q(x)) if the degree of P is

Number of integral solution of ((2x-3)^(2))/(16)<=1 is p and for -4<(x^(2))/(x)<=5 is q then find p and q

If the value of lim_(x->0)( ((3/ x)+1)/((3/x)-1))^(1/x) can be expressed in the form of e^(p/q), where p and q are relative prime then find the value of (p+q) .

Evaluate: (lim)_(x->0)sin8xcot3x . If it is of the form p/q , then (p+q)= ?

If lim_(x rarr a)(px+q)/(qx+p)=l and lim_(x rarr0)(px+q)/(qx+p)=m where p,q!=0 then lm is

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.

let f(x)=5 , -oo 1) f(g(x))=5 then find the value of 2p+q

lim_(x rarr0)(p^(x)-q^(x))/(tan x)