If `f(x)=x((e^(|x|+[x])-2)/(|x|+[x]))` then (where [.] represents the greatest integer function) `(lim)_(xvec0^+)f(x)=-1` b. `(lim)_(xvec0^-)f(x)=0` c. `(lim)_(xvec0^)f(x)=-1` d. `(lim)_(xvec0^)f(x)=0`

Evaluate: ("lim")_(xvec0)(tanx)/x where [dot] represents the greatest integer function

Given ("lim")_(xvec0)(f(x))/(x^2)=2,w h e r e[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

Let f(x)=(x^2-9x+20)/(x-[x]) (where [x] is the greatest integer not greater than xdot Then (a) ("lim")_(xvec5)f(x)=1 (b) ("lim")_(xvec5)f(x)=0 (c) ("lim")_(xvec5)f(x)does not exist (d)none of these

(lim)_(xvec(-1^)/3)1/x[(-1)/x]= (where [.] denotes the greatest integer function) a. -9 b. -12 c. -6 d. 0

If f(x)={x+1/2, x<0 2x+3/4,x >=0 , then [(lim)_(x->0)f(x)]= (where [.] denotes the greatest integer function)

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

If f(x)=|x-1|-[x],w h e r e[x] is the greatest integer less then or equal to x , then a. f(1+0)-1,f(1-0)=0 b. f(1+0)=0=f(1-0) c. ("lim")_(xvec1)f(x)e xi s t s d. ("lim")_(xvec1)f(x)doe snote xi s t

Evaluate: ("lim")_(xvec2)(x-2)/((log)_a(x-1))

If f(x)={{:((sin[x])/([x])","" ""for "[x]ne0),(0","" ""for "[x]=0):} where [x] denotes the greatest integer less than or equal to x. Then find lim_(xto0)f(x).

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. 199