Chapter 4.6, Problem 87E

Solution

(a)

To calculate : The distance between one pixel and the next to the nearest hundredth.

The distance between one pixel and the next pixel is $0.07$ .

Given information :

  $Xmin=0$ and $Xmax=2\pi$ and move the cursor along the x-axis.

Calculation :

Using calculator,

One pixel is at $x=3.2753$ .

The second pixel is at $x=3.3421$ .

The difference is,

  $\begin{array}{c}3.3421-3.2753=0.0668\\ \approx 0.07\end{array}$

Therefore, the distance between one pixel and the next pixel is $0.07$ .

(b)

To calculate : The period of $f\left(x\right)=\sin 250x$ . The number of cycles between two adjacent pixels.

The graphs produced are therefore inaccurate, since so much detail is lost.

Given information :

The period is the length of one full cycle of the graph.

Calculation :

Consider $f\left(x\right)=\sin 250x$ .

Find the period $T$ . Since, the period of sine function is $2\pi$ .

  $\begin{array}{c}f\left(x+T\right)=\sin \left(250\left(x+T\right)\right)\\ =\sin \left(250\left(x\right)+2\pi \right)\end{array}$

Therefore, the period of the required function is,

  $\begin{array}{c}T=\frac{2\pi }{250}\\ =\frac{\pi }{125}\end{array}$

The number of cycles between each pixel,

  $\begin{array}{c}\frac{0.07}{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$125$}\right.}=2.66\\ \approx 3\end{array}$

Therefore, the graphs produced are therefore inaccurate, since so much detail is lost.