Find two functions f(x) and g(x) such that limx→0 ?

Find two functions f(x) and g(x) such that limx→0
f(x) and limx→0
g(x) do not exist
but limx→0
[f(x) + g(x)] does exist.

1 Answer
Feb 13, 2018

Please see below.

Explanation:

You should have an example of a function #h(x)# for which #lim_(xrarr0)h(x)# does not exist.

#1/x# #" "# and #" "# #sin(pi/x)# are two common examples.

You also know some functions for which the limit at #0# does exist. (Like #x^2# or #5x+2# and so on.)

Build each #f(x)# and #g(x)# using a function whose limit does exist and a function whose limit doesn't. (You can even use the same functions for both of them.)
Make sure to add the function whose limit does not exist in one case and subtract it in the other. That way when you add #f(x)+g(x)#, the "problem" parts will cancel.