lim-x-0-x-3-cos-x-sin-2-x-x-2- Tinku Tara June 4, 2023 Limits 0 Comments FacebookTweetPin Question Number 148849 by EDWIN88 last updated on 31/Jul/21 limx→0+x3−cosxsin2xx2=? Answered by iloveisrael last updated on 01/Aug/21 limx→0+x3−sin3x+sin3x−cosxsin2xx2=limx→0+x3−sin3xx2+limx→0+sin2x(sinx−cosx)x2=limx→0+(x−sinx)(x2+xsinx+sin2x)x2+limx→0+(sinx−cosx)=limx→0+(x−sinxx3).x3(x2+xsinx+sin2x)x2−1=limx→016x3(x2+xsinx+sin2x)x2−1=16[limx→0+(x(x2+xsinx+sin2x)]−1=−1. Answered by mathmax by abdo last updated on 01/Aug/21 limx→0+x3−cos(x)sin2xx2=limx→0x−cos(x)(sinxx)2=0−cos(0)×(1)2=−1 Terms of Service Privacy Policy Contact: info@tinkutara.com FacebookTweetPin Post navigation Previous Previous post: show-that-log-a-ab-log-b-ab-logab-a-logab-b-Next Next post: let-a-b-c-x-y-and-z-be-complex-numbers-such-that-a-b-c-x-2-b-c-a-y-2-c-a-b-z-2-if-xy-yz-zx-1000-and-x-y-z-2016-find-the-value-of-xyz- Leave a Reply Cancel replyYour email address will not be published.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.
![lim_(x→0^+ ) ((x^3 −sin^3 x+sin^3 x−cos (√x) sin^2 x)/x^2 ) =lim_(x→0^+ ) ((x^3 −sin^3 x)/x^2 )+lim_(x→0^+ ) ((sin^2 x(sin x−cos (√x)))/x^2 ) =lim_(x→0^+ ) (((x−sin x)(x^2 +x sin x+sin^2 x))/x^2 )+lim_(x→0^+ ) (sin x−cos (√x) ) =lim_(x→0^+ ) (((((x−sin x)/x^3 )). x^3 (x^2 +x sin x+sin^2 x))/x^2 )−1 =lim_(x→0) (((1/6)x^3 (x^2 +x sin x+sin^2 x))/x^2 )−1 =(1/6)[lim_(x→0^+ ) (x(x^2 +x sin x+sin^2 x)]−1= −1.](https://www.tinkutara.com/question/Q148870.png)
