Question

f(x)=e^x+x^2
sa se demonstreze ca functia f nu are asimptota spre +infinit

Answer 1

Calculam limita spre +∞

$\lim_{x \to +\infty} e^x+x^2=+\infty$ ⇒ nu are asimptota orizontala

Vom calcula asimptota oblica

y=mx+n

$m= \lim_{x +\to \infty} \frac{f(x)}{x}\\\\ m= \lim_{x+ \to \infty} \frac{e^x+x^2}{x}=Aplicam\ L'Hopital$

Derivam numitor, derivam numarator

$m= \lim_{x+\to \infty}e^x+2x=+\infty$⇒ nu avem asimptota oblica

Un alt exercitiu gasesti aici: https://brainly.ro/tema/5947358

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