`lim_(x->0^+) (tan(2x))` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply,...

`lim_(x->0^+) (tan(2x))` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Textbook Question

Chapter 4, 4.4 - Problem 56 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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When `x->0^+,` 2x also `->0^+.` And tan(y) is continuous at 0 as an elementary function inside its domain. Therefore

`lim_(x->0^+)(tan(2x)) = tan(0)` = 0.

l’Hospital’s Rule isn't necessary.

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