Question

How do you find the limit of `(-2x^2+x)/x` as x approaches 0?

Answer 1

1

Explanation:

If we substitute x = 0 into the function we obtain `0/0`
which is indeterminate.

However, factorising the numerator gives:

`(x(-2x+1))/x=(cancel(x) (-2x+1))/cancel(x)=-2x+1`

now `lim_(xto 0)(-2x+1)=0+1=1`

`rArrlim_(xto 0)(-2x^2+x)/x=1`