Exercise
$\lim_{x\to0}\left(1+tan2x\right)^{\frac{4}{x}}$
Step-by-step Solution
Learn how to solve simplify trigonometric expressions problems step by step online. Find the limit of (1+tan(2x))^(4/x) as x approaches 0. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(1+\tan\left(2x\right)\right). Apply the power rule of limits: \displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}. The limit of a constant is just the constant.
Find the limit of (1+tan(2x))^(4/x) as x approaches 0
Final answer to the exercise
$e^{8}$
Exact Numeric Answer
$2980.957987$