Majmaah University
College of Engineering
Math. ‘105’
Midterm Exam.
Total Marks: 20
Examiner: Dr. Tarek Nabil Ahmed
Time: 2 hour , 8/6/1433
Answer All Questions
Question 1: find the first derivative of the following functions.
(1) y 
x 1
x 2  2x  2
1
(4) y  coth-1( ),
x
,
(2) y  cos 3 (3 x 2  2 x),
(5) y  sinh -1 (3x 2  1),
(7) y  t  sint, x  1  cost
3 1
2x
(3) y  e
ln( 2 x 3  1),
(6) y  x sin x
(8) y 2  xy - x 2  5
(9) y  x 2 tan -1e x
)12 marks)
Question 2: Find equations of tangent and normal lines to the graph of
y  sin x
at (0,0)
)2 marks)
Question 3: If y=sin(2x+3) then prove that y  4y  0
)3 marks)
Question 4: If 2y 3  3x 2 then prove that yy  2 y2 
1
y
)3 marks)
With my best wishes