Grade 12 · Math
Evaluate a rational limit with a removable hole
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Find the limit as x approaches 5 of (x2 − 25)/(x − 5).
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10
Factor x2 − 25 as (x − 5)(x + 5). For x ≠ 5, the quotient is x + 5, whose limit is 5 + 5 = 10. The original quotient is undefined at 5.
A little hint: Factor and cancel only for x away from the approach value; a limit concerns nearby values.
Substitute the approach value to identify the indeterminate form 0/0; it is not itself an answer.
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