Page 230 - Math Grade 12 (Basic)

PROEUS DARA

ti=1Ql2 lim f(x) = lim sinx + -~sinx = -J2 '1
x->0- x-·0- smx

lim f(x) = lim sinx+ sinx = J2 = f(O) '1
x->0+ x-->0+

~J:J~tlm lim f(x) = lim 2x + = a- 2

~msg t~'i§j2JH~J:Jl§Sthti1.f~ x = tRQlS a 2 = 0 ¢:> a = 2

0?: ""
:3. 'Vx :$0 : f(x) = a Sl ~ f(O) = a Sh lim f(x) = a = f(O)
x~o-
.
. 1
lim f(x) = l1m xsm- = 0
X

6. n. ffltJ j(x) = X- 1- sinx

f(O) = -1 <0 , f(rc) = rc-1 >0

f(x) = 0 si2J sinx = x-1

ti:hru j(O) · f(rc)<O si§1 f(x) 'i:flS"i.HlHmtlfltH1.m!'J1§ti.HsitHSlg '1
U ~ M ~
2. 201og x-x = 0 ffltl f(x) = 20log x-x
10 10
"' .
f(x) thH!H'i'l§SthtHsitHSlg (0, +co)
I ""
tRQl2 f(l) = -1 <0 , f(IO) = 20 10 = 10>0

ti:hru f{l) · f(lO)<O sl§'i f(x) 'i:flStHu'i§IDtlntifltHsitHSlg (1, 'i
u
u
~
~
2
7. f(x) = ax +bx+c mtitrnm~g [o, ~]
ti=1Ql2 f(O)·f(~) = c(~a+23b+c) = c(4a+6:+9c)

&R~bm 2a + 3b + 6c = 0 hl'l§'l§b15 4a + 6b + 12c = 0
II
hl'l§'i§ rn 4a + 6b + 9c = -3c
II