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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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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
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$\lim_{x\to0}\left(\left(\frac{1+4\sin\left(x\right)}{1+3\sin\left(x\right)}\right)^{\frac{x\frac{\cos\left(x\right)}{\sin\left(x\right)}}{\sin\left(2x\right)}}\right)$
Learn how to solve problems step by step online. Find the limit of ((1+4sin(x))/(1+3sin(x)))^((xcot(x))/sin(2x)) as x approaches 0. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by x. Divide fractions \frac{\frac{x\cos\left(x\right)}{\sin\left(x\right)}}{\sin\left(2x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Simplify \frac{x\cos\left(x\right)}{\sin\left(x\right)\sin\left(2x\right)}.
