Question

2 Consider x2 if x <0 f (x) = 2x+ 1 if 0x < 2 (a) Determine whether f is continuous on the interval [0, 1]. (b) Determine whether f is right continuous on the interval [0, 1]. (c) Determine whether f is continuous on the interval [1,2].

Answer 1

pivan function flas= 5 x if nao 2 24+, 15 05142. ca) Gius Ppterial Co, II. let a=1, Alow Com, fu) = Lim, 2x 10) = 2014/= 3. Now FCD = 2 (1971=36:04142) :lom f(x) = f0) 2-19 info is contineng at xal, if(9) is continuous on Co, 13. (b) Given interval Co, 1], Now consider lim for) = 800371a1. 2707 im f(1) = 26077) otla) f(0) = 2609717) Since lim fex)=flo). 27070 f) is right continuous at n=0.

uta 2-) © Given imey wal" (0/2392 coisas coup let at @cmpeni) (21 13 ) Now, bino few = ling Can t 1) - ding Cam + 1) * (***po 13 ) =+1= 5. Now, f (a) 1=1969844 .6 .. lin fcase fl2)=57)| – me i fica) is continuous at-q=&.) fcns is continci eus en 21488] L a function form is said to be continuous on an Interval (a, b) 2. it is continuous at any point Ĉ' creo betoeen aan de Ű cas.c3b):