lim-x-1-a-1-x-a-b-1-x-b-with-a-b-R-2- Tinku Tara June 4, 2023 Limits 0 Comments FacebookTweetPin Question Number 118272 by bramlexs22 last updated on 16/Oct/20 limx→1(a1−xa−b1−xb)=with(a,b)∈(R+)2 Answered by mathmax by abdo last updated on 16/Oct/20 letf(x)=a1−xa−b1−xbwedothechangementx−1=t⇒f(x)=f(1+t)=a1−(1+t)a−b1−(1+t)b(x→1⇒t→0)⇒(1+t)a∼1+at+a(a−1)2t2and(1+t)b∼1+bt+b(b−1)2t2⇒⇒f(1+t)∼a1−1−at−a(a−1)2t2−b1−1−bt−b(b−1)2t2=1−t−a−12t2−1−t−b−12t2=−t−b−12t2+t+a−12t2(t+a−12t2)(t+b−12t2)=a−1−b+12t2t2(1+a−12t)(1+b−12t)⇒f(1+t)∼a−b2(1+a−12t)(1+b−12t)⇒limt→0f(1+t)=a−b2⇒limt→1f(x)=a−b2 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: x-a-x-1-a-1-x-dx-Next Next post: y-3y-2y-1-1-e-x- Leave a Reply Cancel replyYour email address will not be published.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.