Consider two function `y=f(x) and y=g(x)` defined as
`f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):}`
`and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxle3),(x^(2)+b+1,,3ltxle4):}`
`underset(xrarr2)(lim)(f(x))/(|g(x)|+1)` exists and f is differentiable at x = 1. The value of limit will be

Consider two functions y=f(x) and y=g(x) defined as f(x)= {[a x^2 +b, 0lexle1],[ bx + 2b, 1ltxle3],[(a-1)x + 2c - 3 , 3ltxle4]} And g(x)={[c x + d , 0le x le 2],[a x+3-c ,2ltxlt3],[x^2+b+1,3lexle4]} Let f be differentiable at x=1a n dg(x) be continuous at x=3. If the roots of the quadratic equation x^2+(a+b+c)alphax+49(k+kalpha)=0 are real distinct for all values of alpha then possible value of k will be a) k in (-1,0) b). k in (oo,0) c). k in (1,5) d). k in (-1,1)

If f(x)={(3x^2+12x-1,-1lexle2),(37-x,2ltxle3):}

Two functions are defined as under, f(x)={(x+1, x le1),(2x+1, 1ltxle2):} g(x)={(x^2, -1lexlt2),(x+2, 2lexle3):} Find fog and gof

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lexle2 3-x ,2ltxle 3

f(x)=5x-4 (0ltxle1) =4x^2-3x (1ltxlt2) test whether f(x) is differentiable at x=1

If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):} , then f(x) is

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A continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

Given , f(x)=x^(2)+ax+3,g(x)=x+band f (x)=underset(nrarroo)(lim)(f(x)+x^(2n)g(x))/(1+x^(2n)) If F (x) is continuous at x = 1 , then -