lim-x-pi-2-2-cos-x-1-x-x-pi-2- Tinku Tara June 3, 2023 Limits 0 Comments FacebookTweetPin Question Number 131769 by liberty last updated on 08/Feb/21 limx→π/22−cosx−1x(x−π2)=? Answered by bemath last updated on 08/Feb/21 limx→π/21x.limx→π/22sin(x−π2)−1x−π2=2π.limh→02sinh−1h=2π.limh→0ln2.2sinh.cosh1=2ln2π=π−1.ln4 Answered by Dwaipayan Shikari last updated on 08/Feb/21 limx→π22−cos(x)−1x(x−π2)=2−sin(π2−x)−1x(x−π2)=1−(π2−x)log(2)−1π2(x−π2)=2log(2)π=log(4)πlimx→0ax=1+xlog(a) Answered by mathmax by abdo last updated on 08/Feb/21 f(x)=2−cosx−1x(x−π2)wedothechangementx−π2=t(sot→o)andf(x)=f(t+π2)=2sint−1t(t+π2)wehave2sint=esintln(2)sint∼t−t36⇒eln(2)sint∼eln(2)(t−t36)∼1+ln(2)(t−t36)⇒f(t+π2)∼ln(2)(t−t36)t(t+π2)=ln(2)(1−t26)t+π2→2ln(2)π(t→0)⇒limx→π2f(x)=2ln(2)π Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: solve-for-x-a-ax-1-b-bx-1-a-b-Next Next post: tan-x-tan-2x-tan-4x-tan-2-n-x- Leave a Reply Cancel replyYour email address will not be published. Required fields are marked *Comment * Name * Save my name, email, and website in this browser for the next time I comment.