F(x) = `{( (sin(a+2)x + sin x)/x , x lt 0), (b , x = 0), (((x + 3x^2 )^(1/3) - x^(1/3))/x^(4/3)), x gt 0):}`
Function is continuous at x = 0, find `a + 2b`.

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 :

The value of p and q for which the function f(x) = {((sin(p+1)x+sinx)/(x), ",",x lt 0),(q, ",", x = 0),((sqrt(x+x^(2))-sqrt(x))/(x^(3//2)), ",", x gt 0 ):} is continuous for all x in R, are

Let f(x) = {{:((a(1-x sin x)+b cos x + 5)/(x^(2))",",x lt 0),(3",",x = 0),([1 + ((cx + dx^(3))/(x^(2)))]^(1//x)",",x gt 0):} If f is continuous at x = 0, then (a + b + c + d) is

If the function f(x) = {{:((sin(k+1)x + sinx)/x, "when " x lt 0),(1//2, "when " x=0 is),((x+2x^(2))^(1//2)/(2x^(3//2)), " when " x gt 0):} continous at x=0 , then the value of k is-

f(x)={((Sin(a+1)x+Sin2x)/(2x),,x lt 0),(b,,x=0),((sqrt(x-bx^3)-sqrtx)/(bx^(5/2) ), , xgt0):} , f(x) is a continous at x=0 then abs(a+b) is equal to

Find the value of a + b if f(x) = {((a e^(1//|x+2|) - 1)/(2-e^(1//|x+2|)),; -3 lt x lt -2), (b,; x = -2), (sin((x^4-16)/(x^5+32)),; -2 lt x lt 0):} is continuous at x = -2.

Find k, if possible, so that f (x)= [{:((ln (2- cos 2x))/(ln ^(2) (1+ sin 3x)),,, x lt 0),(k,,, x=0),((e ^(sin 2x )-1)/(ln (1+ tan 9x)),,, x gt 0):} is continious at x=0.