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Exercise

$\lim_{x\to0}\left(1+x\right)^{\cos\left(x\right)}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to0}\left(\left(1+x\right)^{\cos\left(x\right)}\right)$ by replacing all occurrences of $x$ by $0$

$\left(1+0\right)^{\cos\left(0\right)}$
2

Add the values $1$ and $0$

$1^{\cos\left(0\right)}$
3

The cosine of $0$ equals $1$

$1^{1}$
4

Calculate the power $1^{1}$

$1$

Final answer to the exercise

$1$

Try other ways to solve this exercise

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  • 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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