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Curve Sketching, Integration, Stationary Points and Asymptotes

Please see question attached.

I require full detailed, step by step solutions to each section of this question.

Coursework 2

Question 1

a) For the curve with equation: S 4x/(x^2 + 1) dx

i) Find the position and nature of any stationary points.
ii) Determine whether the function is even, odd (or neither), and find the point(s) where the curve meets the axes.
iii) Does the curve have any vertical or horizontal asymptotes? Explain your conclusions.
iv) Make up tables of signs for y, y' and y''. Use these to help you make a sketch of the curve.

b) Using your sketch of the curve of y= 4x/(x^2 + 1)
i) Shade in the region representing S 4x/(x^2 + 1) dx 2 ---> -2
ii) Without evaluating the integral, explain why its value is zero.


Solution Summary

Questions about curve sketching, integration, stationary points and asymptotes are answered in detail. The solution is comprehensive and well presented.