c) $$ \lim _{x \rightarrow+\infty} \frac{e^{x}+x}{e^{x}-x^{2}} $$

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Calculate the limit $$ \lim_{x\rightarrow+\infty} \frac{e^{x}+x}{e^{x}-x^{2}} $$.
Evaluate the limit by following steps:
- step0: Evaluate using L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{e^{x}+x}{e^{x}-x^{2}}\right)$$
- step1: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{d}{dx}\left(e^{x}+x\right)}{\frac{d}{dx}\left(e^{x}-x^{2}\right)}\right)$$
- step2: Find the derivative:
  $$\lim _{x\rightarrow +\infty}\left(\frac{e^{x}+1}{e^{x}-2x}\right)$$
- step3: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{d}{dx}\left(e^{x}+1\right)}{\frac{d}{dx}\left(e^{x}-2x\right)}\right)$$
- step4: Find the derivative:
  $$\lim _{x\rightarrow +\infty}\left(\frac{e^{x}}{e^{x}-2}\right)$$
- step5: Use the L'Hopital's rule:
  $$\lim _{x\rightarrow +\infty}\left(\frac{\frac{d}{dx}\left(e^{x}\right)}{\frac{d}{dx}\left(e^{x}-2\right)}\right)$$
- step6: Find the derivative:
  $$\lim _{x\rightarrow +\infty}\left(\frac{e^{x}}{e^{x}}\right)$$
- step7: Simplify the expression:
  $$\lim _{x\rightarrow +\infty}\left(1\right)$$
- step8: Evaluate:
  $$1$$
La limite de $$ \frac{e^{x}+x}{e^{x}-x^{2}} $$ lorsque $$ x $$ tend vers l'infini est égale à 1.
La limite est 1.

c)

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