Learn how to solve problems step by step online. Find the limit of ((4x^3-8x^2)/(4x^3-1))^((x^2+1)/x) as x approaches infinity. Factor the polynomial 4x^3-8x^2 by it's greatest common factor (GCF): 4x^2. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Multiplying the fraction by \ln\left(\frac{4x^2\left(x-2\right)}{4x^3-1}\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)}}.

Find the limit of ((4x^3-8x^2)/(4x^3-1))^((x^2+1)/x) as x approaches infinity