I'm on my limit!
Shopsuey wants to buy some loaves of bread. When the baker asked him how many loaves he would take, Shopsuey gave him the following paper. How many loaves he took?
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2 solutions
Why does the last line say lim x → 3 ≈ 6 ?
or we can use the L'Hospital Rule.
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Sure, but why should we make it more difficult?
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using L'hospital is more easier to me than factorizing something. Because in this rule we just have to differentiate and nothing else.
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@Trishit Chandra – Could you post a solution using the L'hospital Rule? Thank you.
Since the numerator and denominator both approach 0 , by L'Hôpital's rule, x → 3 lim x − 3 x 2 − 9 = x → 3 lim 2 x = 6 . While this may look neat, it takes more than twice as long to verify the limits are both 0 and then differentiate and evaluate, than it does to simply factor it, since it is of the form a 2 − b 2 .
In other words, it is faster to factor since minimal thought is required; ( x 2 − 9 ) can be factored in a split second if you know that 9 = 3 2 . If you use differentiation, though, it becomes a process of 3 separate evaluations, so even if you can differentiate super-fast, it still requires 2 more evaluations than the factoring method.