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Applying the trigonometric identity: $\cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}$
Learn how to solve limits by direct substitution problems step by step online.
$\lim_{x\to0}\left(\frac{x^3\frac{\cos\left(x\right)}{\sin\left(x\right)}}{1-\cos\left(x\right)}\right)$
Learn how to solve limits by direct substitution problems step by step online. Find the limit (x)->(0)lim((x^3cot(x))/(1-cos(x))). Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Multiplying the fraction by x^3. Divide fractions \frac{\frac{x^3\cos\left(x\right)}{\sin\left(x\right)}}{1-\cos\left(x\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}. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(1-\cos\left(x\right)\right).