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

If f(x)={{:(x-1", "xge1),(2x^(2)-2", "xlt1):},g(x)={{:(x+1", "xgt0),(-x^(2)+1", "xle0):}," and " h(x)=|x|," then "lim_(xto0) f(g(h(x)))" is" _______.

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

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

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

Let f(x)={x-1,-1<=x<0 and x^(2),0<=x<=1,g(x)=sin x and h(x)=f(|g(x)|)+[f(g(x)) Then

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

f(x)={x-1,-1<=x<=0 and x^(2),0<=x<=1 and g(x)=sin x Find h(x)=f(|g(x)|)+|f(g(x))|.

If f(x)=(1)/(x), evaluate lim_(h rarr0)(f(x+h)-f(x))/(h)

If f(x)=(1)/(x),g(x)=(1)/(x^(2)), and h(x)=x^(2), then f(g(x))=x^(2),x!=0,h(g(x))=(1)/(x^(2))h(g(x))=(1)/(x^(2)),x!=0, fog (x)=x^(2) fog(x) =x^(2),x!=0,h(g(x))=(g(x))^(2),x!=0 none of these

If f(x) = {{:(sin x"," x ne npi"," n = 0"," pm1"," pm2","...),(" 2, ""otherwise"):}} and g (x) ={{:(x^(2)+1"," x ne 0","2),(" 4, "x=0),(" 5, "x=2):}},"then" lim_(x to 0) g[f(x)] is ………