If `f(x)={{:(x",",0lexle1),(2-e^(x-1)",",1ltxle2),(x-e",",2ltxle3):}` and `g'(x)=f(x), x in [1,3]`, then```

If f(x)={{:(5x-4",",0ltxle1),(4x^(2)+3ax",",1ltxlt2):}

Let f(x)={{:(3^x","-1lexle1),(4-x","1ltxle4):} then

Let f(x)={{:(3^x","-1lexle1),(4-x","1ltxle4):} then

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

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

Let function f(x) is defined in [-2,2] as f(x)={{:({x}",",-2lexle-1),(|sgnx|",",-1lexle1),({-x}",",1ltxle2):} where {x} and sgn x denotes fractional part and signum functions, respectively. Then the area bounded by the graph of f(x) and x-axis is

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

Let f(x)={(x+1, -1lexle0),(-x,0ltxle1):} then

Let f(x)={(x+1, -1lexle0),(-x,0ltxle1):} then