: If `f(x)={x^2+2,xgeq2 1-x ,x<2a n d` `g(x)={2x ,x >1 3-x , xlt=0,t h e nt h ev a l u eoflim_(x->1)f(g(x))i 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___

I fx+1/x=2,t h e p r i n c i p a l v a l u e o f sin^(-1)x is

x2 +2, X22If f(x) = { 2x , xgt1 11-x, xlt2 and g(x) = 3-, X51' 1. evaluate lim f(g(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

f(x)={(x+1,; xlt1), (2x-3,; xgeq1):}, evaluate lim_(x rarr 1)f(x).

If f(x)=(x-1)/(x+1), g(x)=1/x and h(x)=-x . Then the value of g(h(f(0))) 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" _______.

Evaluate: int_(-1)^1f(x)dx ,w h e r ef(x)={1-2x ,xlt=0 1+2x ,xgeq0 int_(-1)^4f(x)dx ,w h e r ef(x)={2x+8,1lt=xlt=2 6x ,2lt=xlt=4