If `f(x) ={(3x-1), x>=1, (2x+3), x<1}`, `g(x) = {(3-x), x<2, (2x-3), x >= 2}`, then `lim_(x->2) f(g(x))=`

If f: RR -> RR is defined by f(x)={((x-2)/(x^2-3x+2), if x in RR\{1, 2}), (2, if x=1), (1, if x=2):}, then lim_(x->2) (f(x)-f(2))/(x-2)

If f(a) = 2 , f ' (a) = 1 , g (a) = -1 , g'(a) = 2 , then lim_(x to a) (g (x) * f (a) - g (a) * f(x))/( x- a) is equal to

If (x^2+x−2)/(x+3) 1) f(x) then find the value of lim_(x->1) 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) .

If f(x) = (2)/(x-3), g(x) = (x-3)/(x+4) and h (x) = (-2(2x + 1))/(x^(2) + x - 12) , then lim_(x rarr 3) [f(x) + g(x) + h(x)] is equal to :

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