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Nutka1998 [239]
3 years ago
12

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. lim x→9 x − 9

x2 − 81
Mathematics
1 answer:
luda_lava [24]3 years ago
8 0

Without resorting to L'Hopitâl's rule,

\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac{x-9}{(x-9)(x+9)}=\lim_{x\to9}\frac1{x+9}=\frac1{18}

With the rule, we get the same result:

\displaystyle\lim_{x\to9}\frac{x-9}{x^2-81}=\lim_{x\to9}\frac1{2x}=\frac1{18}

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