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Numerade Educator



Problem 27 Medium Difficulty

Use Newton's method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations.

$ 4e^{-x^2} \sin x = x^2 - x + 1 $


$x \approx 0.21916368, x \approx 1.08422462$


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Video Transcript

question 27. We start with a function of work. He the negative X It's weird sign thanks equals X squared minus X less one. That's my function. Oh, my affects. I'm gonna bring everything Go on. Sign F of X equals work E with negative X Where so, Damon X minus X squared plus X minus one zero and my pride of X I have you like chain wal. So my changeable is I'm sorry. My product rule I have or e to the negative X square co sign X mine X fine. Thanks minus two eggs less. One Thanks and plus one X to the end minus FX over brine of eggs. So that gives me or e to the negative X squared Finamex. It's weird. What's X minus? I'm getting except in minus Who didn't have to rewrite over it. So I have over X prime, which is for e to the negative. X squared Time co sign Thanks minus two X sign X because of the chain pool and minus two X once and now I can see when I grab that that I have closed 2.2 and closed 1.1. I'm glad you two different ex of one 0.2. And when I point to in for my ex value and should be approximately, I get 0.218832 73 When I love that in for my ex value, I get it. 21916 357 And when I put that in for my ex value, I get it. Oh, 0.219 163 68 And that also equals my exit. Five about you? No. So that's when I stopped my ex of one for my 1.1. I put that in for my ex value and I get 1.8 432 830 I put that in for my ex value and I get 1.84 chip you 462 And I get the same thing for except for So I stopped there. Moves are my two answers