Questions: Assume that postage for sending a first-class letter in the United States is 0.34 for the first ounce (up to and including 1 oz) plus 0.22 for each additional ounce (up to and including each additional ounce). Complete parts (a) through (c).

Assume that postage for sending a first-class letter in the United States is 0.34 for the first ounce (up to and including 1 oz) plus 0.22 for each additional ounce (up to and including each additional ounce). Complete parts (a) through (c).
Transcript text: Assume that postage for sending a first-class letter in the United States is $\$ 0.34$ for the first ounce (up to and including 1 oz ) plus $\$ 0.22$ for each additional ounce (up to and including each additional ounce). Complete Darts (a) throuah (c).
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Solution

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Solution Steps

Step 1: Define the Cost Function

The cost function for sending a first-class letter in the United States is defined as follows: \[ f(w) = \begin{cases} 0.34 & \text{if } 0 < w \leq 1 \\ 0.34 + 0.22 \cdot (w - 1) & \text{if } w > 1 \end{cases} \]

Step 2: Evaluate the Cost at 3 Ounces

To find \( \lim_{w \rightarrow 3.3} f(w) \), we first evaluate \( f(3) \): \[ f(3) = 0.34 + 0.22 \cdot (3 - 1) = 0.34 + 0.22 \cdot 2 = 0.34 + 0.44 = 0.78 \]

Step 3: Determine the Limit

Since the function \( f(w) \) is piecewise constant between whole numbers, we conclude that: \[ \lim_{w \rightarrow 3.3} f(w) = f(3) = 0.78 \]

Final Answer

\(\boxed{0.78}\)

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