Final answer to the problem
Step-by-step Solution
How should I solve this problem?
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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: $\displaystyle{\lim_{x\to a}f(x)^{g(x)} = \lim_{x\to a}f(x)^{\displaystyle\lim_{x\to a}g(x)}}$
Learn how to solve limits of exponential functions problems step by step online.
${\left(\lim_{x\to0}\left(\frac{\ln\left(1+x\right)}{3\sqrt[3]{1+x}-1}\right)\right)}^{\lim_{x\to0}\left(\frac{x}{\sin\left(x\right)^2}\right)}$
Learn how to solve limits of exponential functions problems step by step online. Find the limit of (ln(1+x)/(3(1+x)^(1/3)-1))^(x/(sin(x)^2)) as x approaches 0. 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)}}. Evaluate the limit \lim_{x\to0}\left(\frac{x}{\sin\left(x\right)^2}\right) by replacing all occurrences of x by 0. The sine of 0 equals 0. Calculate the power 0^2.
