Exercitii recapitulative

Licuricy la data de Mier Feb 22, 2012 12:41 am

Fie $f:\mathbb{R}^*\rightarrow \mathbb{R},f(x)=\frac{x^2+ax +3}{x}$ . Daca dreapta y=bx+2 este asimptota a funtiei f,atunci :
a) a+b=3; b) $a*b$ =3; c)2a+b=3 d) $a^2+b^2=3$
nu inteleg ce trebuie sa aflu!

**Admin** la data de Joi Feb 23, 2012 12:07 am

Este vorba de asimptote oblice:

Citind aceste aspecte teoretice, ca sa rezolvam problema, trebuie sa determinam coeficienții ecuației date:
$\begin{array}{l} m = \mathop {\lim }\limits_{x \to \infty } \frac{{f\left( x \right)}}{x} = \mathop {\lim }\limits_{x \to \infty } \frac{{f\left( x \right)}}{x} = \mathop {\lim }\limits_{x \to \infty } \frac{{\frac{{{x^2} + ax + 3}}{x}}}{x} = \mathop {\lim }\limits_{x \to \infty } \frac{{{x^2} + ax + 3}}{{{x^2}}} = 1 \Rightarrow b = 1\\ n = \mathop {\lim }\limits_{x \to \infty } \left( {f\left( x \right) - m \times x} \right) = \mathop {\lim }\limits_{x \to \infty } \left( {f\left( x \right) - 1 \times x} \right) = \mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + ax + 3}}{x} - x} \right) = \mathop {\lim }\limits_{x \to \infty } \left( {\frac{{{x^2} + ax + 3 - {x^2}}}{x}} \right)\\ \mathop {\lim }\limits_{x \to \infty } \left( {\frac{{ax + 3}}{x}} \right) = a \Rightarrow a = 2\\ a + b = 2 + 1 = 3 \end{array}$

Exercitii recapitulative

Exercitii recapitulative

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