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Exercise

$\lim_{x\to+00}\:\frac{\ln\left(e^x-x\right)}{x}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to+00}\left(\frac{\ln\left(e^x-x\right)}{x}\right)$ by replacing all occurrences of $x$ by $+00$

$\frac{\ln\left(e^{+00}- +00\right)}{+00}$

Final answer to the exercise

$\frac{\ln\left(e^{+00}- +00\right)}{+00}$

Try other ways to solve this exercise

  • Choose an option
  • Solve using L'Hôpital's rule
  • Solve without using l'Hôpital
  • Solve using limit properties
  • Solve using direct substitution
  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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