Math Problem Statement
g(x) =
(3sin x) /x if x < 0 a − 4x if x ≥ 0
Solution
The function is defined as a piecewise function. Let's break it down:
\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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Piecewise Functions
Trigonometric Functions
Linear Functions
Formulas
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Theorems
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Suitable Grade Level
Grades 11-12