Question

Determine lim sin(x)/(x²-x)

x⇒0
if possible
Please explain how you know

Answer 1

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

`\displaystyle\lim_(x\to0)(\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
`\frac1{x-1}` is continuous at
`x=0`, so its value is -1, and so the overall limit has a value of 1*(-1) = -1.