Question

Find the limit. Use l'Hospital's Rule if appropriate. If there is a more elementary method, consider using it. lim x→0 (csc(x) − cot(x))

Answer 1

Answer:

0

Step-by-step explanation:

$\lim_{x \to 0} (csc(x)-cot(x))\\= \lim_{x \to 0}(\frac{1}{sin x}-\frac{cos(x)}{sin (x)} )\\=\lim_{x \to 0}(\frac{1-cos x}{sin x} )\\=\lim_{x \to 0}(\frac {2 sin ^2 \frac{x}{2}}{2sin \frac{x}{2} cos\frac{x}{2} } )\\=\lim_{x \to 0}(tan \frac{x}{2} )\\=\lim_{x \to 0}\frac{tan \frac{x}{2} }{\frac{x}{2} } \times \frac{x}{2} \\=1 \times 0\\=0$