Calculus of a Single Variable, Chapter 8, 8.7, Section 8.7, Problem 11

lim_(x->3) (x^2-2x-3)/(x-3)
To solve, plug-in x = 3.
lim_(x->3) (x^2-2x-3)/(x-3) = (3^2-2*3-3)/(3-3)=0/0
Since the result is indeterminate, to get the limit of the function as x approaches 3, apply the L'Hopital's Rule. To do so, take the derivative of the numerator and the denominator.
lim_(x->3) (x^2-2x-3)/(x-3) = lim_(x->3) ((x^2-2x-3)')/((x-3)') = lim_(x->3) (2x-2)/1
And, plug-in x=3.
= (2*3-2)/1 =4

Therefore, lim_(x->3) (x^2-2x-3)/(x-3)=4 .

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