Use limits to verify that the function $y=(x-3)/(x^2-x)$ has a vertical asymptote at $x=0$ ? Want to verify that $lim_(x ->0)((x-3)/(x^2-x))=infty$ ?

Question

1754 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-02-03T12:01:58

See graph and explanation.

As $x to 0_+, y=1/x-2/(x-1) to -oo+2=-oo$

As $x to 0_-, y to oo+2=oo$ .

So, the graph has the vertical asymptote $uarr x=0 darr$ .

graph{(1/x-2(x-1)-y)(x+.001y)=0 [-10, 10, -5, 5]}

Use limits to verify that the function y=(x-3)/(x^2-x)y=(x-3)/(x^2-x)has a vertical asymptote at x=0x=0? Want to verify that lim_(x ->0)((x-3)/(x^2-x))=inftylim_(x ->0)((x-3)/(x^2-x))=infty?