Limits Problem #1

Calculus Level 2

lim ⁡ x → 4 x − 4 x 2 − 16 = ? \lim_{x\to 4} {{x-4}\over {x^2 - 16}} = \ ?


The answer is 0.125.

Just C by Just C , 15, Hong Kong

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3 solutions

Just C
Oct 7, 2020

Factorize as: x − 4 ( x − 4 ) ( x + 4 ) = 1 ( x + 4 ) \displaystyle{{x-4}\over{(x-4)(x+4)}} = {{1}\over{(x+4)}} . Then, we can substitute x = 4 x = 4 into the equation. 1 4 + 4 = 1 8 = 0.125 \displaystyle{1 \over {4 + 4}} = {{1} \over {8}} = 0.125 .

1 Helpful 1 Interesting 1 Brilliant 0 Confused
Marvin Kalngan
Oct 9, 2020

0 Helpful 0 Interesting 0 Brilliant 0 Confused

lim ⁡ x → 4 x − 4 x 2 − 16 = lim ⁡ x → 4 x − 4 ( x − 4 ) ( x + 4 ) = lim ⁡ x → 4 1 x + 4 = 1 8 \displaystyle \lim_{x \to 4} \frac{x-4}{x^2-16} = \lim_{x \to 4} \frac{x-4}{(x-4)(x+4)} = \lim_{x \to 4} \frac{1}{x+4} = \boxed{\frac{1}{8}}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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