Question

-0. (incorrect) 8. (1 point) Compute the following limits using l'Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote 1 - cos(8x) lim x+01 – cos(7x) 8x – 7* – 1 lim x² - 1 Answer(s) submitted: toy (incorrect) 9. (1 point) Compute the following limit using l’Hôpital's rule if appropriate. Use INF to denote oo and MINF to denote -0. lim 7 sin(x) ln(x) = x ot Answer(s) submitted:

Answer 1

son 8 Case) since caso =) Let L lim I-Cos (82) xto I-Costie) How applying L'Hopital rule, ato La lim da (1-C088) d (1-6876) la case) apply L'- Hopital sule 8 sinda " Sino= lim 30 1 Sin7x Again, we lim me are 18 Sinde) ato Gsinta) da L = lim 6ч CS 3G ya Costa T ato - 64 Caso чQ Co-go 64 L ५ Hence lim 1-Cosda 64 19 xoto I-cosrx Aug

lo case) (5) let L= lim 82_72_1 eti -] We apply L'- Hopital ruleia L = lim e s 18%_y x1) \ (x²-1) dx Since I (82) = 8% 118 and d (G²) = ylhan (x²) 8x In 8 Inn lim ex = 6/ ده gu | کد 8 in (8)_7 Int) 2 lim 8x_ya, 8 ln (0)-7 InG) 2 xxl -1 Aug

L= lim sink). In(a) xxot L=7 lim sin(a) la case.) Ktot In(a) Now, we apply L-Hopital rule: 7 lim. d l sine) xxt - - Links da linces U L=7 lim xto Casa -1 (Inxje d. Ince) da cosa L-lim Kalot x. (1na? > 7 lim xxot x xshot Cosa a x L (inky?cos 7. Casx) L=7 lim (11125%c92) Since the absolute value of cosx is not greater than a then Inge & sellnes) Now talking the limits , lim (1-x (112) ²) a lima (nel cosx.slim alma)? s limx. (luzasu do Since the limits are equal, then by squeeze lim allucefcast we have xxo slot Xtot astot Theorem: cost=0 xxot

Therefore lim lim 7 Inley sinazo stot Hence lim 7 Ince) In(a) sin(a) Aug TX ot