Questions: Suppose that the cost, p, of shipping a 3-pound parcel depends on the distance shipped, x, according to the function p(x) depicted in the graph. Find each limit, if it exists. lim x → 500− p(x), lim x → 500 p(x), lim x → 500+ p(x) A. 5 ; 10,10 B. 5 , does not exist; 10 C. 5 ; 5 ; 10 D. 5 ; does not exist, does not exist

Suppose that the cost, p, of shipping a 3-pound parcel depends on the distance shipped, x, according to the function p(x) depicted in the graph. Find each limit, if it exists.

lim x → 500− p(x), lim x → 500 p(x), lim x → 500+ p(x)

A. 5 ; 10,10
B. 5 , does not exist; 10
C. 5 ; 5 ; 10
D. 5 ; does not exist, does not exist

Transcript text: Suppose that the cost, $p$, of shipping a 3-pound parcel depends on the distance shipped, $x$, according to the function $p(x)$ depicted in the graph. Find each limit, if it exists. \[ \lim _{x \rightarrow 500^{-}} p(x), \lim _{x \rightarrow 500} p(x), \lim _{x \rightarrow 500^{+}} p(x) \] A. $5 ; 10,10$ B. 5 , does not exist; 10 C. $5 ; 5 ; 10$ D. 5 ; does not exist, does not exist

Solution

Solution Steps

Step 1: Identify the limits to be evaluated

The problem requires evaluating the following limits:

$\lim_{{x \to 500^-}} P(x)$
$\lim_{{x \to 500^+}} P(x)$
$\lim_{{x \to 500}} P(x)$

Step 2: Analyze the graph for $x \to 500^-$

From the graph, as $x$ approaches 500 from the left (i.e., $x \to 500^-$), the value of $P(x)$ appears to approach 5.

Step 3: Analyze the graph for $x \to 500^+$

From the graph, as $x$ approaches 500 from the right (i.e., $x \to 500^+$), the value of $P(x)$ appears to approach 10.

Step 4: Analyze the graph for $x \to 500$

Since the left-hand limit ($\lim_{{x \to 500^-}} P(x) = 5$) and the right-hand limit ($\lim_{{x \to 500^+}} P(x) = 10$) are not equal, the limit $\lim_{{x \to 500}} P(x)$ does not exist.

Final Answer

A. 5; 10; does not exist

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