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)={{:(sinx","" "xnenpi", "ninI),(2","" ""otherwise"):} and g(x)={{:(x^(2)+1","" "xne0", "2),(4","" "x=0),(5","" "x=2):} then find lim_(xto0) g{f(x)} .

If F (x) = {{:(-x^(2) + 1, x lt 0),(0,x = 0),(x^(2) + 1,x gt = 0):} , .then lim_(x to 0) f(x) is

If f(x)=sgn(x)={(|x|)/x,x!=0, 0, x=0 and g(x)=f(f(x)), then at x=0,g(x) is

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

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-1,xgeq 1 2x^2-2,x 0-x^2+1,xlt=0,a n dh(x) =|x|,t h e n lim_(x->0)f(g(h(x))) is___

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) 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))

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

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)).