Ministry Of Higher Education
Higher Institute of Engineering
6th of October City
Department of Basic Science
Prep. Year: Final Exam
Mathematics: (Calculus I)
Course Code, BAS 11
Date: January 2011
‫مدينة الثقبفة و العلوم‬
‫) أسئلة فى صفحة واحدة و المطلوة اإلجببة عه كل األسئلة‬5( ‫ االمتحبن‬Marks
‫ سبعبت‬3 :‫الزمه‬
[1]Find y` from the following:
(a) y  2x3  cos x
(b) y  3x.tan x
sin x
(d) y  sinh 1x  tan 1x
(e) y 
x  sinh x
12
(c) y = ln x  log( x 2  1)
(f) x 2  y  2x  3y  0
[2](a)Write the membership table of the statement: S  (A  B`)  (B  C)
(b)Evaluate the following limits:
3 x 1
x  sin x
tan 2x
x 1
(i) Lim
(ii) Lim
(iii) Lim
(iv) Lim
x
x
3
4
x 0 e  e
x 0 x  4x
x 1 ln x
x 1 x  1
[3](a) Sketch the curve of the function f(x) = x3  3x
(b) Find the area of the region between the curve y = sin x , x- axis, x[0, 2π]
4
8
4
4
2 log x
(c) Using trapezoidal rule, compute the integral 
4
4
x
x
4
dx , n = 5
x

2
1
[4](a) Sketch the curve of the function f(x) =
(b) Find the following integrals:
(i)  (3  x 2  2x) dx
1 1
(ii)  (x   )dx
x x2
(iii)  x.3x dx
x
(iv) 
dx
x 2  2x  1
2
[5](a)Compute the length of the curve given by y = 4  x 3 / 2 , x[1, 2]
3
(b)If the region between the curve y  cos2x , x-axis, x[0, π 2] is rotated
about x-axis. Find the volume of the generated solid.
(c) Find the following integrals:
1
π/2
1
x 3 dx
dx
(i) 
(ii) 
2
4

5sin
x
2

1
0
x
Good Luck
Dr. Mohamed Eid
8
3
3
6