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1.3 Limits Involving Infinity
Standards :
MCAZMCAK
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⇒ lnfinite
Limit>
Dxlimsfcxko
|#0oe¥ ¥ixi:*infinite limits involve VERTTCALASYMPHTEI
n@ Limits involving infinity
Nowwearelearninghowtevaluatelimutsoffunclimsasx approaches
infinity Koor - a) graphically lealgebraically .
What we know : whatwearelearningnow :
he,nafH=L timafxtl
: im fcx )=Lx
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Let's consider the function : fat ××k÷
THE#E⇒...
a 94. . .
, - .
20 1 .99
conclusion k±b×xHnI= .5=1
As the xvaluesgo towards infinity, they . Values ' ' tend to go
" &" settle down " at 1
.
BASICH Limits involving infinity is analyzing the end behavior
of a function where they - Value " settle down " to a
specific number .This specific number is called theARENALASYMLPBF .
tea faith #t⇒v
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Examples ] �1� ,Hm a×±^
Othfoxt #[email protected] ✓
^
[ Example }]tM a×3 ⇐lxlmgax'=D .ME
N
[ Exampled Evaluate .
:-3T.in#H=...:2
Dlxinszfcx )[email protected]=2�7�,dngzfkI=1
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±nlalinglmtsagobraicallytoevaluate limits of functions as x approaches a ( or - a)
,the
manipulation technique to use is to divide the numerator & denominatorby the highest degree of x that occurs in the denominator
.
Examples] !nsa3xHx¥I5txT
" in"k¥¥YET,¥E=t±a¥⇒±t¥÷in
t¥s#o÷:#'
¥r¥¥
÷Exeo = F.
Example DtIa↳xYx÷zto to
¥ .¥¥÷st¥=¥iIEt¥x÷t÷¥÷a¥tE÷E= 2
.
Wo to
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Example Dkny.fm#I*
neo '¥t*÷*n¥at¥÷#it±n¥fIE÷=hn 4¥t+£ O ou ax÷s¥+¥=hFatIuEI#=2 .
to Do