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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Rewrite the limit using the identity: $a^x=e^{x\ln\left(a\right)}$
Learn how to solve limits by l'hôpital's rule problems step by step online.
$\lim_{x\to0}\left(e^{\cot\left(x\right)\ln\left(1+5\sin\left(x\right)\right)}\right)$
Learn how to solve limits by l'hôpital's rule problems step by step online. Find the limit of (1+5sin(x))^cot(x) as x approaches 0. Rewrite the limit using the identity: a^x=e^{x\ln\left(a\right)}. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by \ln\left(1+5\sin\left(x\right)\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)}}.
