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lisov135 [29]
3 years ago
5

Determine lim sin(x)/(x²-x)

Mathematics
1 answer:
spin [16.1K]3 years ago
7 0

The limit of a product is equal to the product of limits:

\displaystyle\lim_{x\to0}\frac{\sin x}{x^2-x}=\left(\lim_{x\to0}\frac{\sin x}x\right)\left(\lim_{x\to0}\frac1{x-1}\right)

You should recognize the first limit, which has a value of 1. In the second limit, the expression \dfrac1{x-1} is continuous at x=0, so its value is -1, and so the overall limit has a value of 1*(-1) = -1.

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