General InstructionsIn the following, the parameters a, b, and care constants. For every item, create superimposed (i.e. on the samexy-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 valuesyou 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 theaccompanying explanations in a single PDF file and upload in this file submission bin.Items1. 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 varyinga. As noted earlier, you can choose the values of a, but you should be able to cover various cases interms of magnitudes and signs. Provide an explanation underneath your plot on the effect of a on thegraph.2. Afterwards, start with a fixed value of a, say, a =1. Then create a plot of different curves that willresults by varying b. As noted earlier, you can choose the values of b, but you should be able to covervarious cases in terms of magnitudes and signs. Provide an explanation underneath your plot on theeffect of b on the graph.3. [From this point onwards, follow this pattern of fixing one or more of the other parameters while one isbeing 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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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.

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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

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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