If `f(x)={(sinx, x != npi " and " n in Z), (2, " x=npi):}` and `g(x)={(x^2+1, x != 0),(4,x=0), (5, x=2):}` then `lim_(x->0) g{f(x)}` is

f(x)={x ,xlt=0 1,x=0,then find ("lim")_(xvec0) f(x) if exists x^2,x >0

If f(x)={{:(x","" "xlt0),(1","" "x=0),(x^(2)","" "xgt0):}," then find " lim_(xto0) f(x)" if exists.

Let f(x)={x+1,x >0 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

If f(x)=|{:(sinx,cosx,tanx),(x^(3),x^(2),x),(2x,1,x):}| , then lim_(xto0)(f(x))/(x^(2))=

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))

If f(x)={:{(2x+1,x le 0),(3(x+1),x gt 0):} . Find lim_(x to 0) f(x) and lim_(x to 1) f(x) .

Let f(x)={{:(x+1", "xlgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):} Find the LHL and RHL of g(f(x)) at x=0 and, hence, find lim_(xto0) g(f(x)).

If f(x)={(x^nsin(1/(x^2)),x!=0), (0,x=0):} , (n in I) , then (a) lim_(xrarr0)f(x) exists for n >1 (b) lim_(xrarr0)f(x) exists for n<0 (c) lim_(xrarr0)f(x) does not exist for any value of n (d) lim_(xrarr0)f(x) cannot be determined

f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)' must be