How do you prove that the function #f(x) = [x^2 + x] / [x]# is not continuous at a =0?

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Answer 1 · 2018-05-09T21:51:47

Check below

#f# is not continuous at #0# because #0# #cancel(in)##D_f#

The domain of #(x^2+x)/x# is #RR#* #=RR-{0}#

Answer 2 · 2018-05-09T22:55:06

Expression undefined; #0# in denominator

Let's plug in #0# for #x# and see what we get:

#(0+0)/0=color(blue)(0/0)#

What I have in blue is indeterminate form. We have a zero in a denominator, which means this expression is undefined.

Hope this helps!