CalculusI:FindingLimitsGivenaGraph
Name
Giventhegraphofafunction,findtherequestedvalues.
1)
f (0 ) =
( )
f 3 =
f (-3 ) =
lim f ( x ) =
f ( 1) =
f ( - 1) =
lim f ( x ) =
x -1
lim f ( x ) =
x -3
x 1+
lim f ( x ) =
lim f ( x ) =
x 1-
lim f ( x ) =
x 1
lim
Calculus1
Review:Domain,Range,PiecewiseandLimits(ans)
Name
Block
Date
Fillinthemissinginformationforthefollowingfunctions.
2 x 2 - 3 x +1
3x 2 - 6x
1)f x =
2)f x =
x -2
3 x 2 +x - 4
2x - 1 x - 1
( )
( )
3x (x - 2)
x -2
3x
(
)(
( 3 x +4 ) ( x
( 2 x -
Calculus1
Limits
Giventhegraphofafunction,findtherequestedvalues.
1)
f ( 1) =
f (-3 ) =
f (2 ) =
f (0 ) =
lim f ( x ) =
x
lim f ( x ) =
x 1+
lim f ( x ) =
x -3+
lim f ( x ) =
x 2+
lim f ( x ) =
x 0+
lim f ( x ) =
x -
LessonProblems
lim f ( x ) =
x 1-
lim
CalculusI
Name
LimitsofPiecewiseFunctions&InfinityLimits Block
Date
Findtherequestedlimitsforthepiecewisefunctions.Drawasketchofthegraph.
-3 - x
if x - 2
2x
if - 2 <x 2
1. g ( x ) =
2
x - 4 x +3
if x > 2
g ( .5 ) =
g (-2) =
lim g ( x
)=
lim g ( x
culus 1 Name
1H Worksheet (Evaluating Algebraically and InfiniTy LimiTs) gt 5
mm 3- 2. mféf O 3. mg3 O
x 5x3 + 7X2 9 5 a
. 9X4-7X2-3X X ,
O 5- mm D {YE 6- 9Q
. 3x3+7xz+5x 00 . (1)"_ . 1 D
8-1'1'1 x O 9- 12m {\IE tmework: Find The values of The req
Calculus I Name
Infra +0 Limi'l's Block Da'l'e _
\lXZ +4 2
Given for) = 2_ determine The following.
1) m): J? _ 1 2)f(0)= % I: U
To find out what is happening 1'0 The graph of a function when we cannot
. . I
evaluaie fl' a1' a cerfam value we use a I I'M.
CalculusI
ReviewContinuityataPoint
Determineifthefollowingfunctioniscontinuous.Ifthereisdiscontinuitydeterminethetypeandwhereitoccurs.Ifit
isremovable,writeanewcontinuousfunction.
1.f ( x ) =
4x
2
+4 x - 3
2 x +3
x +1
4.f ( x ) = 2
x -1
2.f ( x ) =- x
3
+
Calculus1
WorksheetContinuityataPoint(C)
ANSWERS
2)Discontinuousat x 1 2 , 1
Asymptotesat x 1 2
Notremovable
1)Continuous
3)Discontinuousat x 2 , 3
Asymptotesat x 2
Notremovable
x 3
5)Discontinuousat x 3 ,removable
x 1
4)Discontinuousat x 4 , 4
Holeat x 4