Question

find lim_{x→0} sin(\frac{1}{x}). enter i for ∞, -i for -∞, and dne if the limit does not exist. answer:

Explanation:

Step1: Analyze the behavior of $\frac{1}{x}$ as $x\to0$

As $x\to0^{+}$, $\frac{1}{x}\to+\infty$; as $x\to0^{-}$, $\frac{1}{x}\to-\infty$.

Step2: Analyze the sine - function behavior

The function $y = \sin(t)$ oscillates between - 1 and 1 as $t\to\pm\infty$. That is, as $t=\frac{1}{x}$ approaches $\pm\infty$ when $x\to0$, the values of $\sin(\frac{1}{x})$ do not approach a single real - number value.

Answer:

DNE