`lim_(x->oo)sqrt((x+cosalpha)/(x+sinalpha))`=

Show that : lim_(xto4)((cosalpha)^(x)-(sinalpha)^(x)-cos2alpha)/(x-4)=cos^(4)alphalog_(e)(cosalpha)-sin^(4)alphalog_(e)(sinalpha)

lim_(x->oo) (x-sqrt(x^2+x))

lim_(x->oo) (x-sqrt(x^2+x))

lim_(x->oo) (x-sqrt(x^2+x))

lim_(x->oo) (x-sqrt(x^2-1))

8. lim_(x->oo)(sqrt(x^2+x)-x)

If π<α<3π2 then sqrt((1-cosalpha)/(1+cosalpha))+sqrt((1+cosalpha)/(1-cosalpha)) is equal to (a) 2/(sinalpha) (b) -2/(sinalpha) (c) 1/(sinalpha) (d) -1/(sinalpha)

lim_(x rarr oo)(sqrt(x)+sqrt(a))/(x+a)

lim_(x rarr oo)(sqrt((x+a)(x+b))-x)

lim_(x->oo)(sqrt(x+sqrt(x))-sqrt(x)) equals