Question

55. Is the function given by \[ F(x)=\left\{\begin{array}{ll} \frac{1}{3} x+4, & \text { for } x \leq 3 \\ 2 x-5, & \text { for } x>3 \end{array}\right. \] continuous at \( x=3 \) ? Why or why not?

          55. Is the function given by
\[
F(x)=\left\{\begin{array}{ll}
\frac{1}{3} x+4, & \text { for } x \leq 3 \\
2 x-5, & \text { for } x>3
\end{array}\right.
\]
continuous at \( x=3 \) ? Why or why not?

55. Is the function given by

F(x)={
(1)/(3) x+4, for x ≤ 3

2 x-5, for x>3
.

continuous at x=3 ? Why or why not?

Added by Lisa H.

Calculus and Its Applications

Marvin L. Bittinger, David J.… 10th Edition

Chapter 1

Instant Answer

Solved by Expert Rukhmani Jain

Step 1

\( F(c) \) is defined. 2. The limit of \( F(x) \) as \( x \) approaches \( c \) exists. 3. The limit of \( F(x) \) as \( x \) approaches \( c \) is equal to \( F(c) \). Show more…

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55. Is the function given by \[ F(x)=\left\{\begin{array}{ll} \frac{1}{3} x+4, & \text { for } x \leq 3 \\ 2 x-5, & \text { for } x>3 \end{array}\right. \] continuous at \( x=3 \) ? Why or why not?