Question

CONSUMER AWARENESS The cost $C$ (in dollars) of making $x$ photocopies at a copy shop is given by the function \[ C(x) = \begin{cases} 0.15x, & \quad 0<x\leq25\\ 0.10x, & \quad 25<x\leq100\\ 0.07x, & \quad 100<x\leq500\\ 0.05x, & \quad x>500 \end{cases} \] (a) Sketch a graph of the function. (b) Find each limit and interpret your result in the context of the situation. (i)\[\lim_{x\to 15} C(x) \] (ii)\[\lim_{x\to 99} C(x) \] (iii) \[\lim_{x\to 305} C(x) \] (c) Create a table of values to show numerically that each limit does not exist. (i)\[\lim_{x\to 25} C(x) \] (ii)\[\lim_{x\to 100} C(x) \] (iii) \[\lim_{x\to 500} C(x) \] (d) Explain how you can use the graph in part (a) to verify that the limits in part (c) do not exist.

Name: Problem 84, Chapter 12: Precalculus with Limits
Uploaded: 2019-07-03T23:13:43-08:00
Duration: 2 min 53 s
Channel: Amrita Bhasin

   CONSUMER AWARENESS The cost $C$ (in dollars) of making $x$ photocopies at a copy shop is given by the function

\[ C(x) =
  \begin{cases}
     0.15x,       & \quad 0<x\leq25\\
     0.10x,       & \quad 25<x\leq100\\
     0.07x,       & \quad 100<x\leq500\\
     0.05x,       & \quad x>500
  \end{cases}
\]

(a) Sketch a graph of the function.

(b) Find each limit and interpret your result in the context of the situation.
(i)\[\lim_{x\to 15} C(x) \] (ii)\[\lim_{x\to 99} C(x) \] (iii) \[\lim_{x\to 305} C(x) \]

(c) Create a table of values to show numerically that each limit does not exist.
(i)\[\lim_{x\to 25} C(x) \] (ii)\[\lim_{x\to 100} C(x) \] (iii) \[\lim_{x\to 500} C(x) \]

(d) Explain how you can use the graph in part (a) to verify that the limits in part (c) do not exist.

Precalculus with Limits

Ron Larson 2nd Edition

Chapter 12, Problem 84

Instant Answer

Solved by Expert Amrita Bhasin

07/03/2019

Step 1

(i) For $\lim_{x\to 15} C(x)$, we use the first function $0.15x$ because $15$ falls in the range $0<x\leq25$. So, $C(15) = 0.15 \times 15 = 2.25$. (ii) For $\lim_{x\to 99} C(x)$, we use the second function $0.10x$ because $99$ falls in the range $25<x\leq100$. Show more…

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CONSUMER AWARENESS The cost $C$ (in dollars) of making $x$ photocopies at a copy shop is given by the function \[ C(x) = \begin{cases} 0.15x, & \quad 0<x\leq25\\ 0.10x, & \quad 25<x\leq100\\ 0.07x, & \quad 100<x\leq500\\ 0.05x, & \quad x>500 \end{cases} \] (a) Sketch a graph of the function. (b) Find each limit and interpret your result in the context of the situation. (i)\[\lim_{x\to 15} C(x) \] (ii)\[\lim_{x\to 99} C(x) \] (iii) \[\lim_{x\to 305} C(x) \] (c) Create a table of values to show numerically that each limit does not exist. (i)\[\lim_{x\to 25} C(x) \] (ii)\[\lim_{x\to 100} C(x) \] (iii) \[\lim_{x\to 500} C(x) \] (d) Explain how you can use the graph in part (a) to verify that the limits in part (c) do not exist.