`f(x)={x ,xlt=0 1,x=0,t h e nfin d("lim")_(xvec0)f(x)x^2,x >0ife xi s t s`

If f(x)={x-1,xgeq1 2x^2-2,x 0-x^2+1,xlt=0,a n dh(x) =|x|,t h e n("lim")_(xvec0)f(g(h(x))) is___

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

f(x)=|cos xx1 2sinxx^2 2xtanxx1| . Then value of (lim)_(xvec0)(f(x))/x is equal to 1 b. -1 c. zero d. none of these

If f(x)=(3x^2+a x+a+1)/(x^2+x-2), then which of the following can be correct ("lim")_(xvec1)f(x)e xi s t s a=-2 ("lim")_(xvec-2)f(x)e xi s t s a=13 ("lim")_(xvec1)f(x)=4/3 ("lim")_(xvec-2)f(x)=-1/3

Let f(x)={cos[x],xgeq0|x|+a ,x<0 The find the value of a , so that ("lim")_(xvec0) f(x) exists, where [x] denotes the greatest integer function less than or equal to x .

If f(x)={x/(s in x),x >0 2-x ,xlt=0 and g(x)={x+3,x<1x^2-2x-2,1lt=x<2x-5,xgeq2 Then the value of (lim)_(xvec0)g(f(x)) a. is -2 b. is -3 c. is 1 d. does not exist

If f(x)={("sin"[x])/([x]),for[x]!=0 0,for[x]=0,w h e r e[x] denotes the greatest integer less than or equal to x , then ("lim")_(xvec0)f(x) is 1 (b) 0 (c) -1 (d) none of these

Let f(x)={[x]x in I x-1x in I (where [.] denotes the greatest integer function) and g(x)={sinx+cosx ,x<0 1,xgeq0 . Then for f(g(x))a tx=0 (lim)_(xvec0)f(g(x)) exists but not continuous Continuous but not differentiable at x=0 Differentiable at x=0 (lim)_(xvec0)f(g(x)) does not exist f(x) is continuous but not differentiable

if f(x)={{:(2+x,xge0),(2-x,xlt0):} then lim_(x to 0) f(f(x)) is equal to

Let f(x) be a polynomial of degree four having extreme values at x""=""1 and x""=""2 . If (lim)_(xvec0)[1+(f(x))/(x^2)]=3 , then f(2) is equal to : (1) -8 (2) -4 (3) 0 (4) 4