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#?

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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]}