: 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__`

T h ev a l u eofint_(-2)^2|1-x^2|dxi s_______

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

If f(x)={x^2, for xgeq1x ,for x<0 ,t h e n fof(x) is given by

If f(0)=1,f(2)=3,f(2)=5,t h e nfin dt h ev a l u eof int_0^1xf"(2x)dx

Iff(x)={3x^2+12 x-1,-1lt=xlt=2 37-x ,2

Iff(x)=x+int_0^1t(x+t)f(t)dt ,t h e nt h ev a l u eof(23)/2f(0) is equal to _________

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: RvecR be a function defined by f(x)={[x],xlt=2 0,x >2 where [x] is the greatest integer less than or equal to xdot If I=int_(-1)^2(xf(x^2))/(2+f(x+1))dx ,t h e nt h ev a l u eof(4I-1)i s

A function is reprersented parametrically by the equations x=(1+t)/(t^3); y=3/(2t^2)+2/tdotT h e nt h ev a l u eof|(dy)/(dx)-x((dy)/(dx))^3| is__________

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))