g(x) =

(3sin x)
/x
if x < 0
a − 4x	if x ≥ 0

The function \( g(x) \) is defined as a piecewise function. Let's break it down:

\[
g(x) =
\begin{cases} 
\frac{3 \sin x}{x}, & \text{if } x < 0 \\
a - 4x, & \text{if } x \geq 0 
\end{cases}
\]

### Key Points:
1. **For \( x < 0 \)**: The function is \( \frac{3 \sin x}{x} \). This is a trigonometric function combined with a rational expression.
2. **For \( x \geq 0 \)**: The function is linear, \( a - 4x \), where \( a \) is a constant.

Would you like details on:
- Finding limits for this piecewise function?
- Continuity conditions?
- Solving for \( a \) to make the function continuous?
- Graphing this piecewise function?
  
### 5 Related Questions:
1. How do we find the limit of \( \frac{3 \sin x}{x} \) as \( x \) approaches 0?
2. What is the condition for \( g(x) \) to be continuous at \( x = 0 \)?
3. How does the parameter \( a \) affect the continuity of the function?
4. What is the derivative of \( g(x) \) for each piece of the function?
5. Can the function have a jump discontinuity at \( x = 0 \)?

### Tip:
For piecewise functions, always check the continuity and differentiability at the points where the function changes definition, particularly at \( x = 0 \) in this case.

Explore the piecewise function g(x) = (3sin x) / x for x < 0 and a - 4x for x >= 0. Learn about trigonometric and linear functions, continuity, and limits. Suitable for advanced high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation