Question

Someone can help?? ​

Answer 1

Explanation:

let cos^{-1}x=t

cos t=x

when x=1,cos t=1=cos 0

t \rightarrow 0

`\lim_(x \to 1) (1-√(x))/((cos ^(-1)x)^2 ) \\= \lim_(t \to 0) (1-√(cos~t))/(t^2) * (1+√(cos~t))/(1+√(cos ~t)) \\= \lim_(t \to 0) (1-cos~t)/(t^2(1+√(cos~t)))} \\= \lim_(t \to 0 )(2 sin^2~(t)/(2))/(t^2(1+√(cos~t)))} \\= 2\lim_(t \to 0 )((sin~t/2)/((t)/(2) ))^2 * (1)/(4) * \lim_(t \to 0 )(1)/(1+√(cos~t)) \\=\frac{2}4} * 1^2 * (1)/(1+√(cos~0)) \\=(1)/(2) * (1)/(1+1) \\=(1)/(4)`