`lim_(x rarr oo)(x^(p)+x^(p-1)+1)/(x^(q)+x^(a-2)+2)=(p>0,q>0)`

lim_(x rarr oo)(1)/(x)=0

lim_(x rarr oo)(ax^(2)+b)/(x+1),a>=0

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

lim_(x rarr0)(sqrt(x^(2)+q^(2))-q)/(sqrt(x^(2)+p^(2))-p)

Which of the following is/are true? (a) lim_(x rarr oo)((2+x)^(40)(4+x)^(5))/((2-x)^(45))=1(b)lim_(x rarr0)(1-cos^(3)x)/(x sin x cos x)=(3)/(2)(c)lim_(x rarr0)(ln(1+2x)-2ln(1+x))/(cot^(-1)(sqrt(x+1)-sqrt(x)))=-1 (d) lim_(x rarr oo)(cot^(-1)(sqrt(x+1)-sqrt(x)))/(sec^(1)((2x+1)/((x-1)^(2)))=1)=-1 (d)

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

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

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

f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)), find lim_(x rarr0)f(x)

lim_(x rarr0)(sqrt(4^(2)+p^(2))-p)/(sqrt(x^(2)-q^(2)-q))