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Si ∀x>0\forall x>0, on a :
−2x+3<f(x)<2x+3 -\frac{2}{x} + 3 < f(x) < \frac{2}{x} + 3
alors :
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Si lim⁡x→+∞f(x)=+∞\lim\limits_{x\rightarrow + \infty}f(x)=+\infty   \\  lim⁡x→+∞g(x)=+∞\lim\limits_{x\rightarrow + \infty} g(x)=+\infty
Alors ?
lim⁡x→+∞f(x)g(x)=+∞\lim\limits_{x\rightarrow+\infty}f(x)g(x)=+\infty
lim⁡x→+∞f(x)−g(x)=0\lim\limits_{x\rightarrow+\infty}f(x)-g(x)=0
lim⁡x→+∞f(x)−g(x)=1\lim\limits_{x\rightarrow+\infty}f(x)-g(x)=1
lim⁡x→+∞f(x)g(x)=1\lim\limits_{x\rightarrow+\infty}\frac{f(x)}{g(x)}=1
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Si g(x)−f(x)<0g(x)-f(x) <0
pour tout x>1x>1
et si lim⁡x→+∞g(x)=+∞\lim\limits_{x\rightarrow+\infty}g(x)=+\infty
alors...
lim⁡x→+∞f(x)=+∞\lim\limits_{x\rightarrow+\infty}f(x)=+\infty
lim⁡x→+∞f(x)=0\lim\limits_{x\rightarrow+\infty}f(x)=0
∀x>1,f(x)>0\forall x>1, f(x)>0
lim⁡x→+∞f(x)=−∞\lim\limits_{x\rightarrow+\infty}f(x)=-\infty
ff est bornée.
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Si ∀x>0,\forall x>0,
−2x<f(x)<2x-\frac{2}{x}< f(x)< \frac{2}{x}
alors :
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Parmis les limites suivantes, laquelle vaut 00 ?
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Parmis les limites suivantes, laquelle est une forme indéterminée?
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Quelle est l'asymptote horizontale de
f:x↦3x−42x−5f:x \mapsto \frac{3x-4}{2x-5}?
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Combien vaut lim⁡x→+∞2x2−5x+16x2−5\lim\limits_{x \rightarrow+\infty} \frac{2 x^{2}-5 x+1}{6 x^{2}-5} ?
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Combien vaut
lim⁡x→+∞2x+1−x\lim\limits_{x \rightarrow + \infty} \sqrt{2x + 1} - \sqrt{x} ?
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Combien vaut lim⁡x→5x−1−2x−5\lim\limits_{x \rightarrow 5} \frac{\sqrt{x-1}-2}{x-5} ?
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