CONFIDENTIAL 1 CS/JUL 2022/MAT421
UNIVERSITI TEKNOLOGI MARA
FINAL ASSESSMENT
COURSE : CALCULUS 1
COURSE CODE : MAT421
ASSESSMENT : JULY 2022
TIME : 3 HOURS
INSTRUCTIONS TO CANDIDATES
1. This question paper consists of five (5) questions only.
2. By the end of three (3) hours, you will have another 30 minutes to upload your answer in pdf
form. Submit your answer script according to instruction from your lecturer.
3. Answer ALL questions in English.
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO
This examination paper consists of 8 printed pages
© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
, CONFIDENTIAL 2 CS/JUL 2022/MAT421
QUESTION 1
2
a) Determine the domain of the function f ( x ) = .
3x − 4 − 2
(5 marks)
b) Evaluate each of the following limits by using the limit laws.
sin2 x − x cos2 x
i) lim
x →0 tan2 x
(6 marks)
2 x 2 − 13 x + 15
ii) lim
x →5 5−x
(3 marks)
x 2 + 12 − 4 2x 3 − 6
c) Given f ( x ) = and g ( x ) = 3 . Find lim f ( x ) + lim g ( x ) .
x −2 x +1 x →2 x →
(6 marks)
QUESTION 2
x
a) Find f ( x ) for f ( x ) = using the definition of derivative.
5x − 2
(5 marks)
b) Given the function In ( 2 x + 1) + y 2sin x = 4 y + 10
dy
i) Find using implicit differentiation.
dx
5
ii) Find the slope of the tangent line to the function at point 0, − .
2
(8 marks)
2 dy d 2y
c) If y = e x , show that 2 x 2 − x 2 = −2 xy .
dx dx
(5 marks)
© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
UNIVERSITI TEKNOLOGI MARA
FINAL ASSESSMENT
COURSE : CALCULUS 1
COURSE CODE : MAT421
ASSESSMENT : JULY 2022
TIME : 3 HOURS
INSTRUCTIONS TO CANDIDATES
1. This question paper consists of five (5) questions only.
2. By the end of three (3) hours, you will have another 30 minutes to upload your answer in pdf
form. Submit your answer script according to instruction from your lecturer.
3. Answer ALL questions in English.
DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO
This examination paper consists of 8 printed pages
© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
, CONFIDENTIAL 2 CS/JUL 2022/MAT421
QUESTION 1
2
a) Determine the domain of the function f ( x ) = .
3x − 4 − 2
(5 marks)
b) Evaluate each of the following limits by using the limit laws.
sin2 x − x cos2 x
i) lim
x →0 tan2 x
(6 marks)
2 x 2 − 13 x + 15
ii) lim
x →5 5−x
(3 marks)
x 2 + 12 − 4 2x 3 − 6
c) Given f ( x ) = and g ( x ) = 3 . Find lim f ( x ) + lim g ( x ) .
x −2 x +1 x →2 x →
(6 marks)
QUESTION 2
x
a) Find f ( x ) for f ( x ) = using the definition of derivative.
5x − 2
(5 marks)
b) Given the function In ( 2 x + 1) + y 2sin x = 4 y + 10
dy
i) Find using implicit differentiation.
dx
5
ii) Find the slope of the tangent line to the function at point 0, − .
2
(8 marks)
2 dy d 2y
c) If y = e x , show that 2 x 2 − x 2 = −2 xy .
dx dx
(5 marks)
© Hak Cipta Universiti Teknologi MARA CONFIDENTIAL
