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Exercise

$\lim_{x\to\left|\frac{\pi}{4}\right|}\left(tgx\right)^{tg2x}$

Step-by-step Solution

1

Evaluate the limit $\lim_{x\to{\left|\frac{\pi }{4}\right|}}\left(\tan\left(x\right)^{\tan\left(2x\right)}\right)$ by replacing all occurrences of $x$ by $\left|\frac{\pi }{4}\right|$

$\tan\left(\left|\frac{\pi }{4}\right|\right)^{\tan\left(2\left|\frac{\pi }{4}\right|\right)}$

Final answer to the exercise

$\tan\left(\left|\frac{\pi }{4}\right|\right)^{\tan\left(2\left|\frac{\pi }{4}\right|\right)}$

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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Main Topic: Limits of Exponential Functions

Those are limits of expressions of the form f(x)^g(x).

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