MATH019-Section 2 Intoauchon t Limits.. Limits an=7An important_ida mat mill x uschl in Mmmar fuve. 0 .....
1=23 limf(x=1
F(=UndcAnef(z=3 limf(x)1 limf(x=DNE.(DosNo+Exis1) RH! him f(x=) 11mf(x=3 x-.2+ mFxL 66 NOT EQVAL-DNE 7Ud Lry wry=i=(x)jwm 7H7 R x3a! LHL Rim_xL n<Lx7d wrg x3a
Lim flx);L +VEX 7=(01)
x7at F(avn&8.0K
More on Limits
c17 S1 bsyvox&dx x sx J j5 IUy mL:UyQ Written_&im f(x)=L.mans haY as x.gets close to^(apppaches)
Lim=L ovevallimip xaa LHL RHL -LimFCX-L=imfx xsa x5a
7
7=#
Limf(x)=L
*f(a)=vndesined
f(a)=M
ZHL i=(x wnY Xim F=DNe blc LHL=L#M=RHL
Numerical ApDrach m Limits 1-=3 12-1 X-I F(=un&ehned X 0 a 99 1 101 2 fx I1.9[1.9a(n02.0 3 LHL
Alatbraically looking at limits 2mF(x)= x-9a F(a=f(a=L (any nimber) Umr6=L x3a
There is a limit, move wrk Simplify a factr.i hnd Jne limit. >fa% Thrl may or may not hx a linif.":
Ex. a &im 4x+1=13 -33 F(3=43+1=12+=13
Zt=xh+x 6 lim x72 X- F2=2+4212 4ty-12 2-2 2-2
lim x+6)(x 3 =+2=+xw=
Sechon 2.2 Par+2
Limits as x
"End xhavor of the fnchon"
y wM to 7as x guts )aYgy in me posive divechon
OSX ats laral in me neaakv direckon
a
Looka+fx=
imfx=&m=O X70
&imfx=Lim=D -0 0
As
ralty 70
Also oitx w =0
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=0