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ج
Q1. Complete the following questions using the shown figure for the function
f x. [1 0 Mark]
(a) The domain of
f x
(b) The range of
f x
(c) the domain of − f ( x ) ………………………..
(d)
f − 2 = …………..
(e)
f x is discontinuity at x =
(f)
f x is one to one in the interval
(g)
1
f 0
−
(h) If ( ) ( ( ))
2
g x = x +2, then f g 2
(k) Sketch the inverse of
f x
in the interval
\
Ministry of Higher Education
Higher Institute for Engineering and Technology at Manzala
First Semester: 2023/2024 Date: 11 /1 1 /
Midterm Exam Level: 0
Department: Basic Science Time allowed: 6 0 min
Total Marks: 40 Code: BS 011
Course title: Mathematics 1 Examiner: Dr. Hamouda Abueldahab
رقم المسلسل اسم الطالب:
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Q 2. Answer by True or False [ 3 Mark]
N 0 True (T) or False (F)
1 cos (cos
− 1
2 The range of the function 𝑦 =
equal 𝑦 ∈
5 csc
− 1
4 = sin
− 1
9 sin (sin
− 1
10 𝑇ℎ𝑒 𝑝𝑒𝑟𝑖𝑜𝑑𝑒 𝑜𝑓 𝑦 = |𝑠𝑖𝑛𝑥| is 𝑝 = 2 𝜋
Q 3. Expand 4 + x , if it's known that x 4
[ 3 Mark]
Q 4. Complete [ 3 Mark]
sin 5 x sin 3 x =................................
Q 5. Solve this equation: [ 3 Mark]
1
cos(2sin ( ))
x
−
Q 6. If the roots of the equation
3 2
roots and the value of
. [ 5 Mark]
Q 7. Calculate
where
2
f ( x ) = x − 1 , g x = x + 1
[ 3 Mark]
Q 8. Prove that
1
2
tan
d
x
dx x
−
, then find the first derivative of [ 5 Mark]
1
y tan sin x
−
Q 9. Sketch the function
f x = 5 cos2 x + 1 , then complete the table. [ 5 Marks]
Domain
Range
Symmetry
Zeros
Period