`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`.

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 values of p and q for which the function : f(x) = {{:((sin (p + 1)x + sin x)/(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: 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 :

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

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

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

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.

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.