Post on 30-Apr-2020
This was created by Keenan Xavier Lee - 2014. See my website for more information, lee-apcalculus.weebly.com.
14 Squeeze Theorem
Standards :
MCAZ
MCAZA
This was created by Keenan Xavier Lee - 2014. See my website for more information, lee-apcalculus.weebly.com.
o@ Calculating Limits Algebraically
aximuxI5edmnEEhxeIaxhnaxtt.1t1-2.WnstoEIx-FIieoknErxII.oEEI.tIxkIxExEk-Htxt2tt3.4niXt2-9-x-tEcxrIItxiFtETIEztI-lxmtxfI-rtI-EE.n@SqueezetheoremLetsconsiderxlingox2sinext.5ometimeswecannAfindlimittsdlieoHylbyalgebraicmanipulatioh.sothesqueezetheoremCorYandwiohtheoremYcanhe1p.5upposewehave2functionslrepresentedgraphically.9HhHgkWKtAls9letssaythereisafunoHnfcxjthatThMlNMisBandwiuhedbelweenthe2fundimsA.k
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This was created by Keenan Xavier Lee - 2014. See my website for more information, lee-apcalculus.weebly.com.
Fequeethremlfgcxtfcxtkforallxfainsomeintervalabouta,and
t±a94=tmaK'' =L ,
then limfkkl .
x a
Gangbacktothe previous situation .
lxinoxsinfg )
noteiweknowthatvaluesofsinefnnaionlie between - 1and1.
^
tntoxlgmjosinext Uusetthis ! Am. 1±x2sin#< 1 #-1×21×2sinkx )< 1×2
l '
×hm jx2=0 and,km ox2=o
Sqthesqulezetheoremgvexlimgox 's .in#=O .
This was created by Keenan Xavier Lee - 2014. See my website for more information, lee-apcalculus.weebly.com.
ExampleD If 3×441×3+2 for 01×12,evaluate xlignfcx) .
him 3x =3 (1) =3
÷xM 1×3 +2=43+2--3
Since both limits equal 3, then applying the Squeeze Theorem gives thatkin fcx) =3 .
x.ExampleD Find
lxingyfcx) given that 4 Ifk ) e X +6×-3 for all x .
him 4 = 4-
÷thtx 46×-3=(112+64) -3=4So
, ,Y;n±fcxI=4 when the squeeze theorem is applied .