Find the constant $a$ such that the function
$f ( x ) = \left\{ \begin{array} { r r }
- 4 \cdot \frac { \sin x } { x } , & x

Question

Find the constant $a$ such that the function 
$f ( x ) = \left\{ \begin{array} { r r } 
- 4 \cdot \frac { \sin x } { x } , & x < 0 \
a + 7 x , & x \geq 0
\end{array} \right.$is continuous on the entire real line.
A) 1
B) $- 7$
C) $7$
D) $4$
E) $- 4$

Quizplus · Accepted Answer

For $f(x)$ to be continuous on the entire real line, the two pieces of the function must equal each other at $x=0$. Since $\lim_{x \to 0} -4 \cdot \frac{\sin x}{x} = -4$, we set $a + 7(0) = a = -4$. Therefore, $a = -4$ ensures continuity.

Find the Constant aaa Such That the Function f(x)={−4⋅sin⁡xx,x<0a+7x,x≥0f ( x ) = \left\{ \begin{array} { r r } - 4 \cdot \frac { \sin x } { x } , & x < 0 \\a + 7 x , & x \geq 0\end{array} \right.f(x)={−4⋅xsinx​,a+7x,​x<0x≥0​

Find the Constant $a$ Such That the Function $f ( x ) = \left\{ \begin{array} { r r } - 4 \cdot \frac { \sin x } { x } , & x < 0 \\a + 7 x , & x \geq 0\end{array} \right.$