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Exercise

$\lim\:_{x\to\:\:+\infty\:\:}\left(e^{3x}-5x\right)^{\frac{2}{senx}}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to+\infty}\left(\left(e^{3x}-5x\right)^{\frac{2}{\sin\left(x\right)}}\right)$ by replacing all occurrences of $x$ by $+\infty$

$\left(e^{3\cdot +\infty}-5\cdot +\infty\right)^{\frac{2}{\sin\left(+\infty\right)}}$

Final answer to the exercise

$\left(e^{3\cdot +\infty}-5\cdot +\infty\right)^{\frac{2}{\sin\left(+\infty\right)}}$

Try other ways to solve this exercise

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  • Solve using limit properties
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  • Solve the limit using factorization
  • Solve the limit using rationalization
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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