Assessment 1 SET 1 Quest PDF

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OCT 2020 - JAN 2021QUIZ 1MAT183: CALCULUS 1NAME: ___________________________________________________________________STUDENT NUMBER: __________________ PROGRAMME CODE: __________________GROUP: ___________________________ DATE OF TEST: ______________________LECTURER: __________________________________...

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MAT183_OBE OCT 2020 - JAN 2021

QUIZ 1 MAT183: CALCULUS 1

15

NAME: ___________________________________________________________________ STUDENT NUMBER: __________________ PROGRAMME CODE: __________________ GROUP: ___________________________

DATE OF TEST: ______________________

LECTURER: ______________________________________________________________

At the end of this test, student will be able to state the properties of function, limits, continuity and techniques of differentiation and also capable to compute limits, continuity and derivatives using the approximate methods.

QUESTION CO1:LO1

1 (7m)

2 (8m)

SCORE

INSTRUCTIONS TO CANDIDATE 1. 2.

3. 4. 5.

Answer all questions (30 minutes). Take pictures of your answer sheets using any apps in Android or iOS that can save your picture in one pdf. (Example: CamScanner, Scanbot, Open Note Scanner and NoteBloc). Rename your pdf file as Group_Name_Student ID. For Example, PEC2214P1_Ali Bin Abu_1234567. Students who are caught cheating or suspected of cheating during the examination will be penalized. Answers must be written using pen or else it will not be examined.

~ Be honest with yourself and All the best! ~

MAT183_OBE OCT 2020 - JAN 2021

QUESTION 1

1. Given is the function f. Determine

− x2 f (x) =

x x-3 2

𝐥𝐢𝐦 𝒇(𝒙)

a)

,x 3 ,3 x  6 ,x 6

b)

𝒙→𝟑−

d) 𝒇(𝟔) =

e)

𝐥𝐢𝐦 𝒇(𝒙)

c)

𝐥𝐢𝐦 𝒇(𝒙)

𝐥𝐢𝐦 𝒇(𝒙)

f)

𝐥𝐢𝐦[𝟐𝒇(𝒙)]𝟑

𝒙→𝟑+

𝒙→−∞

𝒙→𝟑

𝒙→𝟒

[7 marks]

QUESTION 2 2 2x − x + 3 a) Evaluate lim 2 x →3

3x − 12x + 9

. [3 marks]

b) Given lim f (x) = − 3 and lim g(x ) = 4 , determine: x →2

x →2

i)

(

lim 2f(x)  9g(x)

x →2

) 2

ii)

lim 3f(x) − 5g(x ) + 16 

x →2

[5 marks]

MAT183_OBE OCT 2020 - JAN 2021

TEST 1 MAT183: CALCULUS 1

30

NAME: ___________________________________________________________________ STUDENT NUMBER: __________________ PROGRAMME CODE: __________________ GROUP: ___________________________

DATE OF TEST: ______________________

LECTURER: ______________________________________________________________

At the end of this test, student will be able to state the properties of function, limits, continuity and techniques of differentiation and also capable to compute limits, continuity and derivatives using the approximate methods.

QUESTION CO1:LO1

1 (12m)

2 (9m)

3 (9m)

SCORE

INSTRUCTIONS TO CANDIDATE 1. 2.

3. 4. 5.

Answer all questions (1 hour). Take pictures of your answer sheets using any apps in Android or iOS that can save your picture in one pdf. (Example: CamScanner, Scanbot, Open Note Scanner and NoteBloc). Rename your pdf file as Group_Name_Student ID. For Example, PEC2214P1_Ali Bin Abu_1234567. Students who are caught cheating or suspected of cheating during the examination will be penalized. Answers must be written using pen or else it will not be examined.

~ Be honest with yourself and all the best! ~

SET1

MAT183_OBE OCT 2020 - JAN 2021

QUESTION 1 [CO1:LO1] Evaluate each of the following limits i)

 x 3 + 6x 2 lim  x→  12 + x2 − 3 x3 

ii)

 3 + 4x 2 lim  2 x→−   2 − 4x

iii)

sec( 2x ) . x→0 6 x cot( 2 x )

  . 

 .  

lim

[12 marks] QUESTION 2 [CO1:LO1]

Given

f (x) =

x2 + 2x + 2 x +t

, x −1 ,-1 x  2

36 - x 2 6+x

,x 2

a) Find the value of t if lim f ( x ) exists. x → −1

b) Determine whether f ( x ) is continuous at x = 2 . [9 marks] QUESTION 3 [CO1:LO1] Given f ( x ) =

3 2−x2

.

a) Find f ' (x ) using the definition of derivative. b) Hence, find the equation of the tangent line to the graph f ( x ) at the point (1, 3) . [9 marks]

SET1...