given f(x) = {3 cos(x), for x≠π; π, for x = π. what is the limit? lim x→π f(x)

Explanation:

Step1: Recall limit - definition

The limit $\lim_{x\rightarrow a}f(x)$ depends on the values of $f(x)$ as $x$ approaches $a$ but not on $f(a)$. Here $a = \pi$, and for $x\neq\pi$, $f(x)=3\cos(x)$.

Step2: Evaluate the limit

We find $\lim_{x\rightarrow\pi}f(x)$ by substituting $x = \pi$ into the expression for $f(x)$ when $x\neq\pi$. So we calculate $\lim_{x\rightarrow\pi}3\cos(x)$. Using the property of the cosine - function $\cos(\pi)=- 1$, we have $3\cos(\pi)=3\times(-1)=-3$.

Answer:

D. -3