Question

evaluate the limit: \\(\lim\limits_{x\to 0} \frac{-6\sin(x)}{5x}\\)

Explanation:

Step1: Recall the standard limit

We know that the standard limit is $\lim_{x \to 0} \frac{\sin(x)}{x}=1$.

Step2: Manipulate the given limit

The given limit is $\lim_{x \to 0} \frac{-6\sin(x)}{5x}$. We can rewrite this as $-\frac{6}{5}\lim_{x \to 0} \frac{\sin(x)}{x}$.

Step3: Substitute the standard limit

Substitute $\lim_{x \to 0} \frac{\sin(x)}{x} = 1$ into the expression. So we have $-\frac{6}{5}\times1$.

Answer:

$-\frac{6}{5}$