Final answer to the problem
Step-by-step Solution
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- Solve using L'Hôpital's rule
- Solve without using l'Hôpital
- Solve using limit properties
- Solve using direct substitution
- Solve the limit using factorization
- Solve the limit using rationalization
- Integrate by partial fractions
- Product of Binomials with Common Term
- FOIL Method
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Apply the power rule of limits: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$
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${\left(\lim_{x\to\infty }\left(8\right)\right)}^{\lim_{x\to\infty }\left(x-3\right)}$
Learn how to solve problems step by step online. Find the limit of 8^(x-3) as x approaches infinity. 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. Evaluate the limit \lim_{x\to\infty }\left(x-3\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 8.
