If `f(x)=lim_(n->oo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1)))` where `[y]` denotes largest integer `lt=,` then identify the correct statement(s). (a)`lim_(n->oo)f(x)=0` (b) `lim_(n->pi/2)f(x)=(3pi)/4` (c)`f(x)=(3x)/2AAx in [0,pi/2]` (d) `f(x)=0AAx in (pi/2,(3pi)/2)`

If f(x)=(lim)_(nvecoo)(3/2+[cosx](sqrt(n^2+1)-sqrt(n^2-3n+1))) where [y] denotes largest integer lt=, then identify the correct statement(s). ("lim")_(nvecoo)f(x)=0 ("lim")_(nvecpi/2)f(x)=(3pi)/4 f(x)=(3x)/2AAx in [0,pi/2] f(x)=0AAx in (pi/2,(3pi)/2)

If (x)=lim_(n rarr oo)((3)/(2)+[cos x](sqrt(n^(2)+1)-sqrt(n^(2)-3n+1))) where [y] denotes largest integer <=, then identify the where [y] denotes largest integer <=, then identify the correct statement(s).(a) lim_(n rarr oo)f(x)=0 (b) lim_(n rarr(pi)/(2))f(x)=(3 pi)/(4)(c)f(x)=(3x)/(2)AA x in[0,(pi)/(2)](d)f(x)=0AA x in((pi)/(2),(3 pi)/(2))

f(x)=lim_(n rarr oo)sin^(2n)(pi x)+[x+(1)/(2)], where [.] denotes the greatest integer function,is

Let g(x)=f(tanx)+f(cotx),AAx in ((pi)/(2),pi). If f''(x)lt0,AAx in ((pi)/(2),pi), then

Let g(x)=f(tanx)+f(cotx),AAx in ((pi)/(2),pi). If f''(x)lt0,AAx in ((pi)/(2),pi), then

lim_(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

lim_(n->oo)cos^2(pi(3sqrt(n^3+n^2+2n)-n)) where n is an integer,equals

If f(x)=lim_(n rarr oo)(tan pi x^(2)+(x+1)^(n)sin x)/(x^(2)+(x+1)^(n)) then

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)

If f(x)=lim_(n->oo)[2x+4x^3+6x^5++2n x^(2n-1)] (0ltxlt1) then int f(x)dx is equal to: