Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![General Instructions
In the following, the parameters a, b, and care constants. For every item, create superimposed (i.e. on the same
xy-axes) graphs of the given functions when the constants are varied. Take note that this entails multiple plots,
one for each of the varied constant (see explanation in item 1 below). You may choose the representative values
you want to use for plotting. You may want to explore the effect of the magnitude (very large vs. intermediate vs.
very small) and the signs (positive, negative, or possibly zero) of the constants. Place all your graphs and the
accompanying explanations in a single PDF file and upload in this file submission bin.
Items
1. Linear function, y = ax + b.
1. Start with a fixed value of b, say, b = 1. Then create a plot of different curves that will results by varying
a. As noted earlier, you can choose the values of a, but you should be able to cover various cases in
terms of magnitudes and signs. Provide an explanation underneath your plot on the effect of a on the
graph.
2. Afterwards, start with a fixed value of a, say, a =1. Then create a plot of different curves that will
results by varying b. As noted earlier, you can choose the values of b, but you should be able to cover
various cases in terms of magnitudes and signs. Provide an explanation underneath your plot on the
effect of b on the graph.
3. [From this point onwards, follow this pattern of fixing one or more of the other parameters while one is
being varied in the subsequent items.]
2. Quadratic function, y = ax2 + bx + c where a +0 (otherwise, it will become linear).
3. Sine function, y = a sin(bt), where a + 0.
4. Exponential function (natural), y = aebz, where a + 0.
5. Logarithmic function (natural), Y= a In(bx), a 0 and b + 0.](https://content.bartleby.com/qna-images/question/86f38f49-e762-4dc7-a395-be18f88891db/40e72b53-1868-4477-b0ae-6f443d9f1868/m0g3b2_processed.png)
Transcribed Image Text:General Instructions
In the following, the parameters a, b, and care constants. For every item, create superimposed (i.e. on the same
xy-axes) graphs of the given functions when the constants are varied. Take note that this entails multiple plots,
one for each of the varied constant (see explanation in item 1 below). You may choose the representative values
you want to use for plotting. You may want to explore the effect of the magnitude (very large vs. intermediate vs.
very small) and the signs (positive, negative, or possibly zero) of the constants. Place all your graphs and the
accompanying explanations in a single PDF file and upload in this file submission bin.
Items
1. Linear function, y = ax + b.
1. Start with a fixed value of b, say, b = 1. Then create a plot of different curves that will results by varying
a. As noted earlier, you can choose the values of a, but you should be able to cover various cases in
terms of magnitudes and signs. Provide an explanation underneath your plot on the effect of a on the
graph.
2. Afterwards, start with a fixed value of a, say, a =1. Then create a plot of different curves that will
results by varying b. As noted earlier, you can choose the values of b, but you should be able to cover
various cases in terms of magnitudes and signs. Provide an explanation underneath your plot on the
effect of b on the graph.
3. [From this point onwards, follow this pattern of fixing one or more of the other parameters while one is
being varied in the subsequent items.]
2. Quadratic function, y = ax2 + bx + c where a +0 (otherwise, it will become linear).
3. Sine function, y = a sin(bt), where a + 0.
4. Exponential function (natural), y = aebz, where a + 0.
5. Logarithmic function (natural), Y= a In(bx), a 0 and b + 0.
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