Exercise 1: Finding lim(x->3) (x^2-9)/(x-3) — Possible Solution
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STEP 1: TRY DIRECT SUBSTITUTION
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At x=3: (3^2-9)/(3-3) = 0/0 - undefined, an indeterminate form,
exactly like this chapter's own worked example.

STEP 2: FACTOR AND SIMPLIFY
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x^2 - 9 factors as (x-3)(x+3) (difference of squares).

(x^2-9)/(x-3) = (x-3)(x+3)/(x-3) = x+3, valid for all x != 3.

STEP 3: EVALUATE THE SIMPLIFIED FORM AT x=3
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x+3 at x=3 = 6

So the limit, algebraically, is 6.

STEP 4: VERIFY NUMERICALLY FROM BOTH SIDES
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x=2.99:  f(x) = 5.99
x=2.999: f(x) = 5.999
x=3.001: f(x) = 6.001
x=3.01:  f(x) = 6.01

Approaching from below (2.99, 2.999) gives values climbing toward
6; approaching from above (3.001, 3.01) gives values descending
toward 6. Both directions converge on the same value.

RESULT
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lim(x->3) (x^2-9)/(x-3) = 6, confirmed both algebraically (via
factoring) and numerically (from both sides of x=3).

WHY THIS WORKS AS AN ANSWER
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The indeterminate 0/0 form is resolved using the exact same
factor-and-cancel technique this chapter's own worked example used,
and the result is independently cross-checked numerically from both
directions rather than trusting the algebra alone.