If `f(x)={(sinx, x != npi " and " n in I_2), (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

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 ………

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" _______.

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

If f(x)=|{:(x,sinx,cosx),(x^2,tanx,x^3),(2x,sin2x,5x):}| then lim_(x to 0)(f'(x))/x is equal to

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 (x)={x,x 0 and g(x)=f(x)+|x| then lim_(x rarr0^(+))(log_(|sin x|)x)^(g(x))=

Let f(x) = -x^(3) + x^(2) - x + 1 and g(x) = {{:(min(f(t))",",0 le t le x and 0 le x le 1),(x - 1",",1 lt x le 2):} Then, the value of lim_(x rarr 1) g(g(x)) , is........ .