Islamic University of Gaza
Faculty of Science
Calculus A(MATHA 1401)
Date:- 23-10-2013
First midterm Exam
Student name:
Student number:
Instructor name:
Q1
10
Department of Math
Time:1 Hour
Q2
10
Q3
10
Q4
10
Total
40
Solve each of the following equations:(Q1) (i) Solve for x:
2 sin2 x + sin x = 1
(ii) Find the limit: lim √
x→1
1−x
.
x2 + 2x − 3
1
on the interval [0, 2π].
(Q2) (i) Sketch the graph of the function f (x) = 3 cos(2x − π) + 1.
(ii) Complete the following sentences:
1. Domain f (x) =..................................................
2. Range f (x) =...................................................
3. lim f (x) = ...................................................
x→0
4. lim f (x) = ...................................................
x→2
5. Find the average rate of change of f (x) over [−1, 0]...............................
2
(Q3) (i) Use the − δ definition to prove the following limit:
p
lim x2 + 5 = 3
x→2
q
2
(ii) If f (x) = 1 − x9 and g(x) = x+1 . Find the formula for the function
f ◦ g and the domain of f ◦ g.
3
(Q4) Choose the correct answer:1. The number d−11.7e equals:(a)b−11.7c.
(b)−d11, 7e.
(d) −11.
(c)b−11.7c.
2. If f (x) = sec x , then f is
(a)a trigonometric function
function
(c)algebraic function
(b)transcendental
(d)both a and b
3. If f is an odd function and g is even then the function
f (sin x + tan x)
h(x) =
is
g(sin(x))
(a)an odd function
(c)neither even nor odd
(b)an even function
(d)a constant function
4. The period of the function f (x) = cot(
(a) 3π
5
(b) 53
3π
x + 3) is
5
(c)5
(d)
−3
5
5. The function h(x) = −x2 is the function f (x) = x2 with reflection
about
(a)x-axis
(c)origin
(b)y-axis
(d)non of the above
4