Question

Let f(x) = {e^x, x < 0 {x+a, x ≥ 0, is continuous in (−∞, +∞), find a?

Answer 1

See explanation.

Explanation:

The function is:

`f(x)={(e^x;x<0),(x+a;x>=0):}`

For every `x in RR-{0}` the function is continuous.

To make it continuous for all `x in RR` we have to find the value of `a` for which

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

The limit on the left side is `1` and the limit on the right side is `a`, so to make them equal `a` must have the value of `1`

Answer: The function is contnuous for all `x in RR` if `a=1`