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Evaluate the limit $\lim_{x\to\infty }\left(\frac{\left(x+1\right)^2}{4^x}\right)$ by replacing all occurrences of $x$ by $\infty $
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$\frac{\left(\infty +1\right)^2}{4^{\infty }}$
Learn how to solve limits to infinity problems step by step online. Find the limit of ((x+1)^2)/(4^x) as x approaches infinity. Evaluate the limit \lim_{x\to\infty }\left(\frac{\left(x+1\right)^2}{4^x}\right) by replacing all occurrences of x by \infty . Apply a property of infinity: k^{\infty}=\infty if k>1. In this case k has the value 4. Infinity plus any algebraic expression is equal to infinity. Infinity to the power of any positive number is equal to infinity, so \infty ^2=\infty.