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COMPLETE CALCULUS CONTINUITY MATHEMATICS
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DEFINE LEFT AND RIGHT (^) Continuity APPLY DEFINITIONS^ OF^ continuity USUALLY
Is (^) nous
A Function^ f is^ continuous (^) at x a if f a^ is^ Defined Ima text exists Ima text (^) f a
n (^) n T
If
F
CHECKING FOR^ Continuity
e g fix
(^16 0 )
e
w PIECEWISE BE (^) CAREFUL WHERE DEFINITION CHANGES fix l c 1 x (^4) t t 4 F (^) i (^4) 1 fc 1 c^
fly y^2 1m fix C^1
(^1 0) 1m fix 9 2 1 fix c^ 1
fix (^) f a HI f WE 1 f 2 ffisoissout.atx
INTERMEDIATE VALUE^ THEOREM^ IF^ f is^ cornous on^ a^ b THEN FOR^ ANY Y VALUE^ BETWEEN^ f a^ And^ f b^ THERE must BE^ SOME^ x^ VALUE C^ SO^ THAT (^) f c^ K fb f APPLYNG WT^ FINDING ROOTS^ ZEROS e g fix x^ x^1 Show (^) f HAS A Root w (^) 0, 21 f is^ continues f so^7 I
fat z 1 P since (^) fenco a^ fan For^ some c^ it 0,1 (^) f a^ o Bonus EXERCISE EEE (^) ILES FOR a (^) AND b^ THAT MAKE (^) f continuous I (^) is cont on x 1 f x b axe axe is^ cont^ o^ c^ i^ z 2
(^2 1) is cont (^) on 2, (^1) fc i 11 _fix 1 I a b^1 I tt^ fInaxtb atb
(^2) f 2 za b 1 fix za^ b t text 22 29 5 5 a b^ I 1 27 2 b (^) I (^151)
