Free Skill check: Using limits Practice Problems • Learn To Be

Let

\qquad f(x) = \begin{cases} 1+3\cos(2x) &\text{if $x<\pi$}\\ 4+\sin x &\text{if $x\geq \pi\,. $} \end{cases}

Is

f

continuous at the point

x=\pi

? Why?

Choose 1 answer:

A
Yes, because $\displaystyle \lim_{x \to \pi}f(x)= f(\pi)$
B
Yes, because $\displaystyle \lim_{x \to \pi^+} f(x) = \lim_{x \to \pi^-} f(x)$
C
No, because $\displaystyle \lim_{x \to \pi}f(x) \ne f(\pi)$
D
No, because $\displaystyle \lim_{x \to \pi^+} f(x) \ne \lim_{x \to \pi^-} f(x)$

Skill check: Using limits