Limiti notevoli 5
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Exercise:
Determina i valori dei seguenti limiti riconducoli al limite notevole lim_ntoinftynsinfracn visto in classe laddove necessario footnoteSuggerimento: Per la d e la e ti tornerà utile sin^x+cos^x abcmulti abc lim_ntoinftyfracn^+-nsinleftfracn-right abc lim_ntoinftyntanleftfracnright abc lim_ntoinftyn^tanleftfracnrightsinleftfrac-nright abc lim_nto inftyn^left-cosleftfracnrightright abc lim_nto inftynleft-cosleftfracnrightright abc lim_nto inftyfracnleft-cosleftfracnrightrightsinleftfracnright abcmulti
Solution:
abclist abc * lim_ntoinftyfracn^+-nsinleftfracn-right&lim_ntoinftyfracn^+-nn-n-sinleftfracn-right &lim_ntoinftyunderbracefracn^+-n^+n-_to /-underbracen-sinleftfracn-right_to frac-frac-. * abc lim_ntoinftyntanleftfracnrightlim_ntoinftyunderbracensinleftfracnright_to fracunderbracecosleftfracnright_to abc lim_ntoinftyn^tanleftfracnrightsinleftfrac-nrightlim_ntoinftyunderbracefracntanleftfracnright_to -underbracefracn-sinleftfrac-nright_to - abc + e lim_nto inftyn^text o left-cosleftfracnrightright Abbiamo che cosleftfracnrightsqrt-sin^leftfracnright da cui -cosleftfracnright-sqrt-sin^leftfracnrightfrac--sin^leftfracnright+sqrt-sin^leftfracnrightfracsin^leftfracnright+sqrt-sin^leftfracnright A questo punto lim_nto inftyn^left-cosleftfracnrightrightlim_ntoinftyfracn^sin^leftfracnright+sqrt-sin^leftfracnrightfrac+sqrt-frac mentre lim_nto inftynleft-cosleftfracnrightrightlim_ntoinftyunderbracefracn_to underbracefracn^sin^leftfracnright+sqrt-sin^leftfracnright_to / / abc * lim_nto inftyfracnleft-cosleftfracnrightrightsinleftfracnrightlim_nto inftyfracfracnsinleftfracnright fracn nleft-cosleftfracnrightright lim_nto inftyfracunderbracefracnsinleftfracnright_to frac ^ underbraceleftnright^left-cosleftfracnrightright_to frac frac frac fracfrac. * abclist
Determina i valori dei seguenti limiti riconducoli al limite notevole lim_ntoinftynsinfracn visto in classe laddove necessario footnoteSuggerimento: Per la d e la e ti tornerà utile sin^x+cos^x abcmulti abc lim_ntoinftyfracn^+-nsinleftfracn-right abc lim_ntoinftyntanleftfracnright abc lim_ntoinftyn^tanleftfracnrightsinleftfrac-nright abc lim_nto inftyn^left-cosleftfracnrightright abc lim_nto inftynleft-cosleftfracnrightright abc lim_nto inftyfracnleft-cosleftfracnrightrightsinleftfracnright abcmulti
Solution:
abclist abc * lim_ntoinftyfracn^+-nsinleftfracn-right&lim_ntoinftyfracn^+-nn-n-sinleftfracn-right &lim_ntoinftyunderbracefracn^+-n^+n-_to /-underbracen-sinleftfracn-right_to frac-frac-. * abc lim_ntoinftyntanleftfracnrightlim_ntoinftyunderbracensinleftfracnright_to fracunderbracecosleftfracnright_to abc lim_ntoinftyn^tanleftfracnrightsinleftfrac-nrightlim_ntoinftyunderbracefracntanleftfracnright_to -underbracefracn-sinleftfrac-nright_to - abc + e lim_nto inftyn^text o left-cosleftfracnrightright Abbiamo che cosleftfracnrightsqrt-sin^leftfracnright da cui -cosleftfracnright-sqrt-sin^leftfracnrightfrac--sin^leftfracnright+sqrt-sin^leftfracnrightfracsin^leftfracnright+sqrt-sin^leftfracnright A questo punto lim_nto inftyn^left-cosleftfracnrightrightlim_ntoinftyfracn^sin^leftfracnright+sqrt-sin^leftfracnrightfrac+sqrt-frac mentre lim_nto inftynleft-cosleftfracnrightrightlim_ntoinftyunderbracefracn_to underbracefracn^sin^leftfracnright+sqrt-sin^leftfracnright_to / / abc * lim_nto inftyfracnleft-cosleftfracnrightrightsinleftfracnrightlim_nto inftyfracfracnsinleftfracnright fracn nleft-cosleftfracnrightright lim_nto inftyfracunderbracefracnsinleftfracnright_to frac ^ underbraceleftnright^left-cosleftfracnrightright_to frac frac frac fracfrac. * abclist