Math 242: Calculus I

Problem Set 1

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1.1

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The following problems are meant to test and challenge your problem-solving skills. Looking up, buying, or copying the answers won't help you pass your calculus class. Everyone can use the online Discussion Forum to discuss the answers, however do not publish the solutions. Some of them might require considerable time to think through. We can discuss online,

The Four Principles of Problem Solving

• Understand the Problem
• Think of a Plan
• Carry out the Plan
• Look Back

We an do this without outlining the solution online. If you get stuck, join the online discussion. You can use Desmos, Geogebra, or your favorite software to create graphs. List your answers in numerical order.

$$ \begin{align*} 1.&\ \text{Solve the equation } \left| 4x - \left| x+1 \right|\right| = 3. \\ \\ 2.&\ \text{Solve the inequality } |x-1| - |x-3| \ge 5. \\ \\ 3.&\ \text{Sketch the graph of the function } f(x) = \left| \left( x^2 - 4|x| + 3 \right) \right|. \\ \\ 4.&\ \text{Sketch the region in the plane consisting of the points }(x,y)\text{ such that} \\ \\ &\ \qquad\qquad\qquad |x-y| + |x| - |y| \le 2 \\ \\ 5.&\ \text{Sketch the graphs of }f(x)=x\text{, and }g(x)=\frac{1}{x}\text{ on the same axes.} \\ &\ \text{Then in its own axes create a graph of} \\ \\ &\ \qquad\qquad\qquad y = \max\left\{ x, \frac{1}{x} \right\} \\ \\ 6.&\ \text{Sketch the region in the plane defined by the equation} \\ \\ &\ \qquad\qquad\qquad \max\left\{ x, y^2 \right\} = 1 \end{align*} $$

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