Question

Determine a raiz de ƒ(x)=ex−x2 no intervalo de -1 a 0 em x, para ε =0,001.
Escolha uma: a. x = - 0,7038 b. x = - 0,0017 c. x = - 0,1905 d. x = - 0,7253 e. x = - 0,8913

Answer 1

$f(x)=e^x - x^2\\\\f'(x)=e^x -2x$

usando newton raphson
$\boxed{\boxed{x_{(n+1)} = x_n - \frac{f(x_n)}{f'(x_n)} }}$

partindo de x0=-0.5
$\tex{passo 1 }\\x_1= -0.5-\frac{f(-0.5)}{f'(0.5)} \\\\x_1 = -0.7219 \\\\ \tex{passo 2 }\\ x_2= -0.7219 - \frac{f(-0.7219)}{f'(-0.7219)} \\x_2=-0.7036\\\\ \tex{passo 3 }\\ x_3= -0.7036 - \frac{f(-0.7036)}{f'(-0.7036)} \\x_3=-0.7035\\\\\ \tex{passo 4 }\\ x_4= -0.7035 - \frac{f(-0.7035)}{f'(-0.7035)} \\\\x_4=-0.70345$

x= -0.7034  ..a)

Answer 2

x = - 0,7038 é a correta?