Question

Am nevoie de ajutor la puncul c).
Multumesc!

Answer 1

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Answer 2

[tex]\it F(x) =\int(1-x^2+x^4) dx = x-\dfrac{x^3}{3} +\dfrac{x^5}{5} + \mathcal{C} \\\;\\ \\\;\\ Fie\ \mathcal{C} =0 \Rightarrow F(x) = x-\dfrac{x^3}{3} +\dfrac{x^5}{5} = \dfrac{1}{15}(3x^5 -5x^3+15x) \\\;\\ \\\;\\ xf(x) = x(1-x^2+x^4) =x^5-x^3+x[/tex]


[tex]\it \lim \limits_{x \to \infty} \dfrac{xf(x)}{F(x)} = \lim \limits_{x \to \infty} \dfrac{x^5-x^3+x}{\dfrac{1}{15}(3x^5-x^3+x)} = \lim \limits_{x \to \infty} \dfrac{15(x^5-x^3+x)}{3x^5-x^3+x} = \\\;\\ \\\;\\ =\dfrac{15}{3} =5[/tex]