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

0

Explanation:

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