`f(x)=(sinx+cosx)^(c o s e c x) ,-pi/2ltxlt0` `a,x=0` `(e^(1/x)+e^(2/x)+e^(3/|x|))/(ae^(2/x)+be^(3/|x|)), 0ltxltpi/2` continuous at `x=0` find a and b.

If f(x)={((sinx+cosx)^(cosecx),-(pi)/2ltxlt0),(a,x=0),((e^(1/x)+e^(2/x)+e^(3/x))/(ae^(-2+1/x)+be(-1+3/x)), 0ltxlt(pi)/2):} is continuous at x=0 then

Let f(x) be defined as follows: f(x)=[((cosx-sinx)^(cose cx),-pi/2ltxlt0),(a,x=0),(((e^(1/x)+e^(2/x)+e^(3/x))/(ae^(2x)+be^(3x)),0ltxltpi/2)] if f(x) is continuous x=0 , then (a)a=1/e(b)a=e(c) b=1/e (d)b=e

Find the values of a and b if f is continuous at x=0, where f(x)={:{((sinx + cos x)^(cosec x), , - pi/2 lt xlt 0),( a, , x=0 ), ((e^(1//x)+e(2//x)+e^(3//x))/(ae^(-2+1//x ) + be^(-1+3//x)),, 0 lt x lt pi/2):}

Find the values of a and b if f is continuous at x=0, where f(x)={:{((sinx + cos x)^(cosec x), , - pi/2 lt xlt 0),( a, , x=0 ), ((e^(1//x)+e(2//x)+e^(3//x))/(ae^(-2+1//x ) + be^(-1+3//x)),, 0 lt x lt pi/2):}

If f(x) =(e^(1)/(x^(2))+1)/(e^(1)/(x^(2))-1) (x ne 0) is continuous at x = 0 find f(0)

If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0, then f(0) =

If f(x) = (e^(x)-e^(sinx))/(2(x sinx)) , x != 0 is continuous at x = 0, then f(0) =

If f(x)={{:((sqrtx)/(sqrt(4+sqrtx)-a),xgt0),(c,x=0),((4e^((2)/(x))+3e^((1)/(x)))/(e^((2)/(x))+be^((1)/(x))),xlt0):} continuous at x = 0 for some constants a, b and c, then the value of (50b)/(a) is equal to