Exercise
$\lim_{x\to\infty\:}\left(1+\frac{4}{7x}\right)^x$
Step-by-step Solution
Learn how to solve problems step by step online. Find the limit of (1+4/(7x))^x as x approaches infinity. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\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. Rewrite the product inside the limit as a fraction.
Find the limit of (1+4/(7x))^x as x approaches infinity
Final answer to the exercise
$\sqrt[7]{\left(e\right)^{4}}$