How do you find $lim 1/x^2-1/x$ as $x->0$ ?

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Answer 1 · 2017-01-08T13:46:28

$lim_(x->0) 1/(x^2)-1/x = +oo$

You can simplify the function in this way:

$1/(x^2)-1/x = 1/x^2(1-x)$

Now:

$lim_(x->0) 1/(x^2) = +oo$

$lim_(x->0) (1-x) = 1$

So:

$lim_(x->0) 1/(x^2)-1/x = +oo$

graph{1/x^2-1/x [-10, 10, -5, 5]}

How do you find lim 1/x^2-1/xlim 1/x^2-1/x as x->0x->0?