to find the tangent line of the curve, take the derivative, to determine the slope of the tangent line.

y=##sqrt(x^2+4)## y=##(x^2+4)^(1/2)##y’=##1/2####(x^2+4)^(-1/2)##(2x)y’=##x/sqrt(x^2+4)##

because you want the tangent line at x=3, plug it in to y’ to find the slop at that point, since we know that the derivative is the slope at a certain point.

y'(3)=##3/sqrt(3^2+4)##=##3/sqrt(13)##

at x=3, the point on the curve is (3,##sqrt13##)now, you can create the tangent line(y-##sqrt13##)= ##3/sqrt13##(x-3)y-##sqrt13##=##3/sqrt13##x-##9/sqrt13##y=##3/sqrt13##x-##9/sqrt13##+##sqrt13##

so your y-intercept for the tangent line at x=3 would be (##9/sqrt13##+##sqrt13##)

 

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neither

To determine if a function is even/odd consider the following.

• If f(x) = f( -x) , then f(x) is even

Even functions have about the y-axis.

• If f( -x) = – f(x) , then f(x) is odd

Odd functions have symmetry about the origin.

Test for even

##f(-x)=(-x)^3+1=-x^3+1 ≠f(x)##

Since f(x) ≠ f( -x) , then f(x) is not even.

Test for odd

##-f(x)=-(x^3+1)=-x^3-1≠f(-x)##

Since f( -x) ≠ – f(x) , then f(x) is not odd.

##rArrx^3+1″ is neither even nor odd”## graph{x^3+1 [-10, 10, -5, 5]}

 

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How do you determine a long term and short term profit or loss when looking at competitive markets in a micro class

How do you determine a long term and short term profit or loss when looking atcompetitive markets in a micro class150 WORDSIn the business world, it is of sure that competitors will be existing…

 

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how do you design a research study by:- 

1• developing one specific research question and related hypothesis

2• Discuss the importance/significance of your research topic.

3 • Describe your dependent and independent variables to be tested in your study.

4• Describe how you define and measure the variables.

5• Describe other potential explanatory (control) variables in your analysis.

6• Identify your research subjects (persons or things). What or who will be studied?

7 • Describe how you will select the subjects and how you will reach them.

 8• Describe the type of sampling techniques that you will use to select a sample.

 9• Explain why you have selected that sampling method.

10• Describe in detail how you will actually collect the data for your study.

 11• Explain why you choose the method(s)

12• Briefly describe how you will test your hypothesis using the data you collect.

13• Discuss any issues or limitations of your study

 

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How do you describe and explain the historical context of a secondary resoucre? Example: Explain the historical context of the journal American Slavic and East European.

Does this mean to explain the context of the events the article is about from the viewpoint of the time the paper was written or the time the event happens?

 

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