Limits (Advanced)

Limits: core idea

• 1. Evaluate $\lim_{x\to0}\dfrac{\arcsin x-x}{x^3}$.

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• 2. Evaluate $\lim_{x\to0}\dfrac{\arctan x-x}{x^3}$.

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• 3. Evaluate $\lim_{x\to0}\dfrac{e^x-1-x-x^2/2}{x^3}$.

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• 4. Evaluate $\lim_{x\to0}\dfrac{(1+x)^5-1-5x}{x^2}$.

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• 5. Evaluate $\lim_{x\to\infty}\dfrac{x}{\sqrt{x^2+1}+x}$.

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• 6. Evaluate $\lim_{x\to0}\dfrac{\cos(2x)-1}{x^2}$.

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• 7. Evaluate $\lim_{x\to0}\dfrac{\sin x-x\cos x}{x^3}$.

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• 8. Evaluate $\lim_{x\to\infty}x\left(\sqrt{1+\dfrac2x}-1\right)$.

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• 9. Evaluate $\lim_{x\to0}\dfrac{\ln(1+x)-x+x^2/2}{x^3}$.

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