Word Count : 115

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Let $f(x)=\cos x - x e^{x}$. With $x_0=0,\;x_1=1$ we have $$ f(0)=\cos0-0\cdot e^{0}=1, \qquad f(1)=\cos1-1\cdot e^{1}\approx0.5403023059-2.7182818285=-2.1779795226. $$ Secant formula $x_{2}=x_{1}-f(x_{1})\dfrac{x_{1}-x_{0}}{f(x_{1})-f(x_{0})}$. Substituting the numbers, $$ x_{2}=1-(-2.1779795226)\frac{1-0}{-2.1779795226-1} =1-\frac{2.1779795226}{3.1779795226}\approx1-0.685334\approx0.314666. $$ Now _________ _________ ____ ___ ________ _______ ________ _____ ______ ____ ___ __________.
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