Question

1. (9 points) Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = 8(%) R -1 - 1 -2 lim f(x) - lim g(x)- 10 10 lim x-0 g(x) lim f(x) - lim g(x)= lim (f(x) + g(x)]- lim f(x) - lim g(x) - 8(x) lim x- f(x)

Answer 1

(- : f(()) = 1 from giren graph) i] let L- lim fcx) x 0 Then L = fco) -) = - su lim forc) = x-o 2) Now, we exists only when Know, lim fox) xy-1 lim 27-1 fex) = lim foc) and in that case xt-it the value of lim fexs is equal to above Common value. Here, im x-)-1- foxes lim fer means cyprouehing ra with 2 - а values of a ca and ces we approach @ x=8-1 with values of xc @ 1 then fcx) and approaches o Also, similarly lim fex) co X-+ lim actat fesy means approaching a with xa values of xa and as we approcech x= -1 with values of B-1, then f(x) 500 approaches x fexs So, lim fex) =o=lim x-1- X- so, Here, lim fox) x-17 exists and I lim ferc = X-1

3) How, lim xtolt fex) = - 1 as x approaches I with values of x>1 approaches then fes) soi lim fase) = X-) it 45 low, lim gcxy ت to gco) a) lim X70 92x) = 2 (-:900)=2) S} Now, lim Coc) poana! 9-1- lim gcoc means approaching xea with Octa and here as values or xca we cumpraching < -1 x = -1 with values of 168ceea then fotos) gceo approaches Also similarly, lim gox) = 1 ay-it lim goxs means approaching n=a with at at values of x> a and here as we approaching votace with values of ne> -1 then g pesc) cupproaches x = -1

6] How, lim gesc) = + x-) I (..cum as x cupproceenes I with values of x> ges) approaches *>') then 0 Su lim 2-) + ga) = O 75 Now, lim fox) 000 fco) go) сау OFK Call OFIC T = 2- o a lim fox) = 1 and lim gox)=31 go) 2 xto ات lim - 0 fox) goo) = nl - 2 8 now, tim x-)-1 [ fexes + gcxy lim fases + lim gasy X-1 x--) o ti lim x-)-1 fexs=0 cand tim x-1 gasus = 1 lim 2-)-1 [ feses + gases] gj ردی)N lim tit form) goses genry FOXC) 그 lim 9cc ) 2)it im fex) 2+1+ PDO is if lim x-) it foc) 90 Hese, lim x- it fenc) = -1 #0 So, lim WII +EX gox) to goxy fox) xt it = lim xtit fox) oli La lim 06-)1+ gox) fox) = 0