Question

Determine the values of a and b that make f(x) continuous. a=? b=?

Answer 1

`a=7, b=7`

Explanation:

For the function `f(x)` to be continuous at `x=0` we must have

`lim_{x -> 0^-}f(x) = f(0) =lim_{x -> 0^+}f(x)`

Now

`lim_{x -> 0^-}f(x) = lim_{x -> 0^-}7 sinx/x = 7`

`f(0) = a`

and
`lim_{x -> 0^+}f(x)= lim_{x -> 0^+}b cos 4x = b`

Thus , for continuity,

`7 = a = b`