2. (37.4) Use the Maclaurin series for e, cos x, and sinx to prove Euler's formula eie cos 0 + i sin 0.
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- Determine the number of terms necessary to approximate cos x to 8 significant figures using the Maclaurin series approximation cosx = 1 Term 1² x4 tº x8 + + 2 4! 6! 8! Calculate the approximation using a value of x=0.77 rad. Use the rue value of cos 0.7 π =-0.587785252 Show step-by-step solutions per term. Complete the table: Result - E₁ Ea is εRo tind the Power sevies for ě cos.x and tor é^sin x tHam the Sevies ter ex in the Fallawing way: Weite the series for e Put Z-xa yi shou that é'= é(Gsy+ising) take Yeal and imaginary Parts of the . equation, and Put ye y9.If f(t)= t2-2t where 0< t6. Let h be a given number in the interval (0, 7). Find the Fourier cosine series of the function [1 f (x) =- 03.10 Determine the number of terms necessary to approximate cos x to 8 significant figures using the Maclaurin series approximation cos.x = 1 4! 6! 8! Calculate the approximation using a value of x = 0.3. Write a program to determine your result.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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