Learn how to solve problems step by step online. (x)->(0)lim((cos(x)-sin(x))^cot(x)). Wenden Sie die Formel an: \lim_{x\to c}\left(a^b\right)=\lim_{x\to c}\left(e^{b\ln\left(a\right)}\right), wobei a=\cos\left(x\right)-\sin\left(x\right), b=\cot\left(x\right) und c=0. Applying the trigonometric identity: \cot\left(\theta \right) = \frac{\cos\left(\theta \right)}{\sin\left(\theta \right)}. Wenden Sie die Formel an: a\frac{b}{c}=\frac{ba}{c}, wobei a=\ln\left(\cos\left(x\right)-\sin\left(x\right)\right), b=\cos\left(x\right) und c=\sin\left(x\right). Wenden Sie die Formel an: \lim_{x\to c}\left(a^b\right)={\left(\lim_{x\to c}\left(a\right)\right)}^{\lim_{x\to c}\left(b\right)}, wobei a=e, b=\frac{\cos\left(x\right)\ln\left(\cos\left(x\right)-\sin\left(x\right)\right)}{\sin\left(x\right)} und c=0.

(x)->(0)lim((cos(x)-sin(x))^cot(x))