Find constant "b" such that the function is continuous everywhere.

The function Is a piece-wise function. Find the constant "b" that would make this function continuous.

4sin(x)/(x) x < 0
b - 2x x >= 0 (greater than or equal to)

To find the constant, you would set the two functions to equal each other. But when you plug in "0" it ends up being in the denominator and therefore does not exist at zero. Does that mean there is no constant. Could I plug in another number other than 0? I'm confused. Help

Here, you cannot equate the two parts of the function, because they hold on disjoint ranges (x < 0 and x>=0). Instead, you must ensure that the limit of the first function as x -> 0 from the negative side equals the value of the second function at x = 0.

Now lim [x -> 0] 4 (sin(x)/x) = 4

Therefore, the second function must evaluate to 4 at x = 0. Hence b = 4.

lim f(x) = 4 , as x--->0-

as x-->0+ , lim f(x) = b ,and for f(x) continuous b = 4

b = 4