$$Ai=x-aix-ai$$,$$i=1$$,$$2$$,....n, and $$a1$$

Question

$$Ai=x-aix-ai$$,$$i=1$$,$$2$$,....n,    and   $$a1$$

Infinity Learn · Accepted Answer

We have $$Ai=x-aix-ai$$, $$i=1$$,$$2$$,..,n, and $$a10$$ for $$i=1$$,$$2$$,.... , $$m-1and$$ $$Ai=x-ai-x-ai=-1$$ for $$i=m$$, $$m+1$$, ...., n $$Ai=x-aix-ai=1$$ for $$i=1$$,$$2$$,....., $$m-1Sirnilarly$$, ifx is in the right neighborhood af am, then $$x-ai$$<$$0$$ for $$i=m+1$$,..., n and $$x-ai$$>$$0$$ for $$i=1$$,$$2$$,...,m.Therefore, $$Ai=x-ai-x-ai=-1$$ for $$i=m+1$$,...,nand $$Ai=x-aix-ai=1$$ for $$i=1$$,$$2$$,...,mNow, limx→$$am-$$ $$A1A2$$...$$An=-1n-m+1and$$ limx→$$am+$$ $$A1A2$$...$$An=-1n-mHence$$, limx→am $$A1A2$$...An does not exist.We have $$Ai=x-aix-ai$$, $$i=1$$,$$2$$,..,n, and $$a10$$ for $$i=1$$,$$2$$,.... , $$m-1and$$ $$Ai=x-ai-x-ai=-1$$ for $$i=m$$, $$m+1$$, ...., n $$Ai=x-aix-ai=1$$ for $$i=1$$,$$2$$,....., $$m-1Sirnilarly$$, ifx is in the right neighborhood af am, then $$x-ai$$<$$0$$ for $$i=m+1$$,..., n and $$x-ai$$>$$0$$ for $$i=1$$,$$2$$,...,m.Therefore, $$Ai=x-ai-x-ai=-1$$ for $$i=m+1$$,...,nand $$Ai=x-aix-ai=1$$ for $$i=1$$,$$2$$,...,mNow, limx→$$am-$$ $$A1A2$$...$$An=-1n-m+1and$$ limx→$$am+$$ $$A1A2$$...$$An=-1n-mHence$$, limx→am $$A1A2$$...An does not exist.We have $$Ai=x-aix-ai$$, $$i=1$$,$$2$$,..,n, and $$a10$$ for $$i=1$$,$$2$$,.... , $$m-1and$$ $$Ai=x-ai-x-ai=-1$$ for $$i=m$$, $$m+1$$, ...., n $$Ai=x-aix-ai=1$$ for $$i=1$$,$$2$$,....., $$m-1Sirnilarly$$, ifx is in the right neighborhood af am, then $$x-ai$$<$$0$$ for $$i=m+1$$,..., n and $$x-ai$$>$$0$$ for $$i=1$$,$$2$$,...,m.Therefore, $$Ai=x-ai-x-ai=-1$$ for $$i=m+1$$,...,nand $$Ai=x-aix-ai=1$$ for $$i=1$$,$$2$$,...,mNow, limx→$$am-$$ $$A1A2$$...$$An=-1n-m+1and$$ limx→$$am+$$ $$A1A2$$...$$An=-1n-mHence$$, limx→am $$A1A2$$...An does not exist.

Ai=x-aix-ai,i=1,2,....n, and a1

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