Home
Class 12
MATHS
Let f: R to R be a function defined as ...

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 :

A

`-3`

B

`-2`

C

`-3/2`

D

`-5/2`

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

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

Let f(x)={{:((sin(a+1)x+sinx)/(x)",",xlt0),(c",",x=0),((sqrt(x+bx^(2)))/(bx^((3)/(2)))",",xgt0):} If f(x) is continous at x = 0, then

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 .

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

If f(x) is continuous at x=0 , where f(x)={:{((sin (a+1)x+sin x)/(x)", for " x lt 0),(c", for " x=0),((sqrt(x+bx^(2))-sqrt(x))/(b sqrt(x))", for " x gt 0):} , then

The values of a,b and c which make the function f(x)={{:(("sin"(a+1)x+"sinx")/(x),xlt0),(C,x=0),(sqrt(x+bx^(2)-sqrt("x"))/(b"x"^(3//2)),"x"gt0):} continuous at x=0 are

If f(x)={{:((sin(a+1)x+2sinx)/x", "xlt0),(2" ,"x=0),((sqrt(1+bx)-1)/x" ,"xgt0):} is continuous at x = 0, then find the values of 'a' and 'b'.