`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.

Expert Answers
Borys Shumyatskiy eNotes educator| Certified Educator

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.