How do you find the limit lim_(x->5)(x^2-6x+5)/(x^2-25) ?

1 Answer
Gaurav
Jul 29, 2014

=2/5

Explanation

=lim_(x->5)(x^2-6x+5)/(x^2-25) , if we plug x=5, we get 0/0 form

Using Finding Limits Algebraically,

=lim_(x->5)(x^2-5x-x+5)/((x+5)(x-5))

=lim_(x->5)(x(x-5)-1(x-5))/((x+5)(x-5))

=lim_(x->5)((x-5)(x-1))/((x+5)(x-5))

=lim_(x->5)((x-1))/((x+5))

=(5-1)/(5+5)

=4/10=2/5

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