Find a value of c that makes the function continuous at the given value of x. If it is impossible, state this.
- $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { x ^ { 2 } } , & x < 0 \\c , & x = 0 \\3 x , & x > 0\end{array} ; x = 0 \right.$

Question

Find a value of c that makes the function continuous at the given value of x. If it is impossible, state this.
-$$f ( x ) = \left\{ \begin{array} { l l } 
\frac { 4 } { x ^ { 2 } } , & x < 0 \
c , & x = 0 \
3 x , & x > 0
\end{array} ; x = 0 \right.$$
A) 16
B) Impossible
C) -4
D) 4

Quizplus · Accepted Answer

The function is discontinuous at x = 0 because the left-hand limit as x approaches 0 is undefined (since the function involves division by zero), and the right-hand limit is 0. Therefore, no value of c can make the function continuous at x = 0.

Find a Value of C That Makes the Function Continuous f(x)={4x2,x<0c,x=03x,x>0;x=0f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { x ^ { 2 } } , & x < 0 \\c , & x = 0 \\3 x , & x > 0\end{array} ; x = 0 \right.f(x)=⎩⎨⎧​x24​,c,3x,​x<0x=0x>0​;x=0

Find a Value of C That Makes the Function Continuous $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { x ^ { 2 } } , & x < 0 \\c , & x = 0 \\3 x , & x > 0\end{array} ; x = 0 \right.$