`f(x)={(ae^x+be^(-x),-1lexle1),(cx^2,1lexle3),(2ax+c,3lexle4):}` ,f'(0)+f'(2)=e then the value of a is:

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

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

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,,2ltxlt3),(x^(2)+b+1,,3gexle4):} lim_(xrarr2) (f(x))/(|g(x)|+1) exists and f is differentiable at x = 1. The value of limit will be

If a function f:RtoR is defined by f(x){{:(2x,xgt3),(x^(2),1lexle3),(3x,xlt1):} Then the value of f(-1)+f(2)+f(4) is

Suppose that f(x) is a function of the form f(x)=(ax^(8)+bx^(6)+cx^(4)+dx^(2)+15x+1)/(x), (x ne 0)." If " f(5)=2 , then the value of f(-5) is _________.

If f(x)=ax^(2)+bx+c and f(x+1)=f(x)+x+1 , then the value of (a+b) is __

If f(x)={("sin"(pix)/2,, x lt1),(4x-3,,1lexle2),(log2(2x^(2)-4),,2ltxlt3):} then value of lim_(xto1)f(x)+lim_(xto2^(+))f(x) is

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

Let f(x)={(x+1,xle4),(2x+1,4ltxle9),(-x+7,xgt9):} and g(x)={(x^(2),-1lexlt3),(x+2,3lexle5):} then, find f(g(x)) .

f(x)={(|2x-3|[x],0lexle2),(x^(2)/2,2ltxle3):} . If f(x) is defined in (0,3) then ([.] denotes greatest integer function) A. Point of discontiuity at x=1, 1/2,2 B. Point of discontinuity at x=1 and 2 C. Point of non-differentiability at x=1, 1/2,2 D. Point of non-differentiability at x=1, 3/2, 2