Answer the question.
-Is $\mathrm { f }$ continuous at $\mathrm { x } = 0 ?$
$f ( x ) = \left\{ \begin{array} { l l }
x ^ { 3 } , & - 2

Question

Answer the question.
-Is $\mathrm { f }$ continuous at $\mathrm { x } = 0 ?$
$f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 3 } , & - 2 < x \leq 0 \
- 4 x , & 0 \leq x < 2 \
5 , & 2 < x \leq 4 \
0 , & x = 2
\end{array} \right.$

Quizplus · Accepted Answer

To show that $\mathrm { f }$ is continuous at $\mathrm{ x } = 0$, we need to show that:

1. $\mathrm { lim_{x \to 0^-} f(x) = f(0)}$
2. $\mathrm { lim_{x \to 0^+} f(x) = f(0)}$
3. $\mathrm { f }$ is defined at $\mathrm{ x } = 0$.

We can see that

1. $\mathrm { lim_{x \to 0^-} f(x) = lim_{x \to 0^-} x^3 = 0}$
2. $\mathrm { lim_{x \to 0^+} f(x) = lim_{x \to 0^+} (-4x) = 0}$
3. $\mathrm{f(0)}$ is defined as $\mathrm{f(0) = 0}$

Thus, all the conditions for continuity at $\mathrm{ x } = 0$ are met, and $\mathrm{f}$ is continuous at $\mathrm{ x } = 0$. So the answer is A.

Answer the Question f\mathrm { f }f Continuous At x=0?\mathrm { x } = 0 ?x=0?

Answer the Question $\mathrm { f }$ Continuous At $\mathrm { x } = 0 ?$