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

1 Answer
Daniel L.
Jun 23, 2018

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#

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