`f(x)={((3/(x^2))sin2x^2, x lt 0), ((x^2+2x+c)/(1-3x^2), x ge 0 " and "x!=1/(sqrt(3))), (0, if x=1/(sqrt(3))):}` then in order that f be continuous at `x=0,` the value of c is

f(x) = {{:((3)/(x^(2)) Sin 2x^(2) " , if " x lt 0),((x^(2) + 2x + c)/(1-3x^(2) ) " , if " x ge 0 " , " x ne (1)/(sqrt(3))),(0 " , if " x = (1)/(sqrt(3))):} then in order that 'f' be a continuous at x =0 , the value of 'c' is

f(x)={{:((3//x^2)sin2x^2,"if" x lt 0),((x^2+2x+c)/(1-3x^2), "if" x ge 0 "):} then in order that f be continuous at x=0, the value of c is

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Let f(x)={((cos^(2)x-sin^(2)x-1)/(sqrt(x^(2)+4)-2)"," , x ne 0),(a",", x =0):} , then the value of a in order that f(x) may be continuous at x = 0 is

Let f: R to R be a function defined as f(x)={(,(sin (a+1)x+sin 2x)/(2x), if x lt 0),(, b, if x=0), (,(sqrt(x+bx^(3))-sqrtx)/(bx^(5/2)), if x gt 0):} If f is continuous at x=0 then the value of a+b is equal to :

if f(x) = {(x^(3),x <0),(3a + x^(2), x ge 0):} is continuous at x = 0 , then a is

A function f is defined by f(x)= {{:((sin (a + 1) x + sinx)/(x)" if " x lt 0),(c " if " x = 0),(((x + bx^(2))^(1/2)- x^(1/2))/(bx^(3/2)) " if " x gt 0 ):} It f(x) is continuous at x = 0 , find the values of a,b and c .

The function f(x)=((3^(x)-1)^(2))/(sin x*ln(1+x)),x!=0, is continuous at x=0, Then the value of f(0) is

If function defined by f(x) = {{:((sin 3x)/(2x)"," ,x != 0),(k + 1",", x = 0):} is continuous at x = 0 , then value of k is