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

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Answer 1 · 2018-05-09T21:51:47

Check below

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

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!

How do you prove that the function f(x) = [x^2 + x] / [x]f(x)=x2+xxf(x) = [x^2 + x] / [x] is not continuous at a =0?