let-f-x-arcsinx-with-x-0-1-1-prove-that-1-x-2-f-x-xf-x-0-2-prove-that-1-x-2-f-n-2-x-2n-1-x-f-n-1-x-n-2-f-n-x-3-prove-that-f-n-x-0-n- Tinku Tara June 4, 2023 Relation and Functions 0 Comments FacebookTweetPin Question Number 30749 by abdo imad last updated on 25/Feb/18 letf(x)=arcsinxwithx∈[0,1]1)provethat(1−x2)f″(x)−xf′(x)=02)provethat(1−x2)f(n+2)(x)=(2n+1)xf(n+1)(x)+n2f(n)(x)3)provethatf(n)(x)⩾0∀n. Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: Find-lim-n-k-1-n-i-1-k-i-1-4-1-Next Next post: f-function-C-f-1-f-2-let-take-a-k-f-k-0-k-prove-that-a-n-1-1-n-1-k-0-n-a-k-a-n-k- Leave a Reply Cancel replyYour email address will not be published.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.
![let f(x)=arcsinx with x∈[0,1] 1) prove that (1−x^2 )f^(′′) (x) −xf^′ (x)=0 2)prove that (1−x^2 )f^((n+2)) (x)=(2n+1)x f^((n+1)) (x) +n^2 f^((n)) (x) 3) prove that f^((n)) (x) ≥0 ∀n .](https://www.tinkutara.com/question/Q30749.png)