Question

Consider the given and select ALL TRUE statements. There may be one correct answer or some correct answers. Minus points for incorrect selections 1) Graph of f(x) Graph of g(x) 1) 24 1+ 1 2 1 2 34 5422 -1 1 4+ B) lim f(x)g(x) = + A) lim gixx) - - 3 D) lim f(x) g(x) C) Wirm f = g(x)) = X 0 Consider the given and select ALL TRUE statements. There may be one correct answer or some correct answers. Minus points for incorrect selections 2) Suppose that fl-111 R is a function such that fxs 1-cos(x) for all xel-11). 2) A) (0) B) lim fx) - 0 D) f is not continuous at 0. c) lim f(x) - 0 X-01

do 1 and 2

Answer 1

Solution (1) Graph of f(20) goa Ghraph TY 4+ 3 20 2 1 1 1 2 3 $ 32 45 -3 -2 -1 0 -1 2 -2+ .-3+ -45 --3 lim glxflos) = lim glo-F10-)) 170- H-20- = .g 10-4-1) = g(0-) = -3 Therefore lim g(x600) = -3 Trie ao- (B) lim f(a)g(21) = r^2+, F12+)g(2+) - Hoo)(-2) = .00 lim Fla)goo 2->2+ Those force given statment is false. lim f(x) gi) = too =>24. שיחהחה

C) lim (fog)(o) slon f(g(x) = 6 fllem 9(43) xxa Hayor Hor alon F(-3) = +00 N->or Therefore given stectoment is false. O lim Ef(a) + g(x)] = lin fru & dim g(x) H-72- 2172- 22- +27-0. Therefore lim [frastgx] = 0 Answer and ® H-2- True. Giren solution @ f:1-1,73 —R such that 14(39).< 1-c08be9 for all ace [1,1] know that 6) 1211<a -> -a sasa We

Now using above property equation (2) becomes -(1-cosx) < x < 1-CS x Lui) -+-+CoS2 < Cx) <1-cosx Rent a 20 in equation () weget etcoslo) -s flo) <1-coso) -Y+X FOOD & 1-4 0 < (9) < 0 Therfor Foco >True. Now B lem +1 +csx) < lom for < lom (1-cosuj nto x-xo ro 2 7+4 = lin f(x) E A A a> o z lim fra) so urto Therefore lim F 2120 towe. sa Hence tim FX-0 ® is also correct. noyat 0. tim flag = F(o) Therefore if i antinious adxo. 2-70 I Answer: A ® 7