ask 4 Compare Euler's claim about ratios to the definition of the derivative given at the beginning of this project. How are they similar? How are they different? Euler only needed to introduce one more important idea, namely that he will often think of w as a very (very!) small value, and will still be interested in the ratio he described above.
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Euler started with the equation transformed it to and then used geometric series to write it as Show how Euler did his calculation and find his mistake.
Adi S.
a) Research and explain in your own word what is the Euler's method and how it is used in differential equations. The function y = f(x) is a solution to the following differential equation dy/dx = (y ln y) / x , y(2) = e b) Use Euler's method to obtain an approximation to y(4). - You need to choose different step sizes. - You use a method to solve the differential equation and find the exact solution. - For each step size chosen you can find the percentage difference between the exact value and the approximated value and you can comment on the reliability of the estimates. c) Investigate in which situations the Euler's method will give an underestimate and in which situations will give an overestimate. You need to give at least one example for both situations and prove that you get an over- or an under- estimate.
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