If `[dot]` denotes the greatest integer function, then `(lim)_(xvec0)x/a[b/x]` a. `b/a` b. `0` c. `a/b` d. does not exist

If [.] denotes the greatest integer function then lim_(x→0) ​ [x^2/(tanx.sinx)] =

("lim")_(x->0)[(sin(sgn(x)))/((sgn(x)))], where [dot] denotes the greatest integer function, is equal to (a)0 (b) 1 (c) -1 (d) does not exist

If [.] denotes the greatest integer function , then lim_(xrarr0) sin[-sec^2x]/(1+[cos x ]) is equal to

If [dot] denotes the greatest integer function, then find the value of lim_(x->0) ([x]+[2x]++[n x])/(n^2)

Given ("lim")_(xvec0)(f(x))/(x^2)=2, \where\ [dot] denotes the greatest integer function, then (A) ("lim")_(xvec0)[f(x)]=0 (B) ("lim")_(xvec0)[f(x)]=1 (C) ("lim")_(xvec0)[(f(x))/x] does not exist (D) ("lim")_(xvec0)[(f(x))/x] exists

If [f((sqrt(3))/2)] is [.] denotes the greatest integer function) 4 (b) 5 (c) 6 (d) -7

If [.] is the greatest integer function and f(x)=[tan^2x], then (a) ("lim")_(xvec0)f(x) does not exist (b) f(x) is continuous at x=0 (c) f(x) is not differentiable at x=0 (d) f^(prime)(0)=1

If n is a non zero integer and [*] denotes the greatest integer function then lim_(x->0)[nsinx/x] + lim_(x->0)[ntanx/x] equals

(lim)_(x->oo)(sinx)/x equals a. 1 b . 0 c. oo d. does not exist

Column I ([.] denotes the greatest integer function), Column II ""("lim")_(xvec0)([100(sinx)/x]+[100(tanx)/x]) , p. 198 ("lim")_(xvec0)([100 x/(sinx)]+[100(tanx)/x]) , q. 199 ("lim")_(xvec0)([100(sin^(-1)x)/x]+[100(tan^(-1)x)/x]) , r. 200 ("lim")_(xvec0)([100 x/(sin^(-1)x)]+[100(tan^(-1)x)/x]) , s. 201