Given f x = 3 x 4 + 7 x 3 − 12 x 2 − 14 x + 12 , a. How many zeros does f x have (including multiplicities)? b. List the possible rational zeros. c. Determine if the upper bound theorem identifies 2 as an upper bound for the real zeros of f x . d. Determine if the lower bound theorem identifies − 4 as a lower bound for the real zeros of f x . e. Revise the list of possible rational zeros based on the answer to parts (c)and (d). f. Find the rational zeros. g. Find all the zeros. h. Graph the function.
Given f x = 3 x 4 + 7 x 3 − 12 x 2 − 14 x + 12 , a. How many zeros does f x have (including multiplicities)? b. List the possible rational zeros. c. Determine if the upper bound theorem identifies 2 as an upper bound for the real zeros of f x . d. Determine if the lower bound theorem identifies − 4 as a lower bound for the real zeros of f x . e. Revise the list of possible rational zeros based on the answer to parts (c)and (d). f. Find the rational zeros. g. Find all the zeros. h. Graph the function.
Solution Summary: The author explains that the number of zeros in f(x) is equal to the degree of the given equation.
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Automobile Department
Subject :Engineering Analysis
Time: 2 hour
Date:27-11-2022
کورس اول تحليلات
تعمیر )
1st month exam / 1st semester (2022-2023)/11/27
Note: Answer all questions,all questions have same degree.
Q1/: Find the following for three only.
1-
4s
C-1
(+2-3)2 (219) 3.0 (6+1)) (+3+5)
(82+28-3),2-
,3-
2-1
4-
Q2/:Determine the Laplace transform of the function t sint.
Q3/: Find the Laplace transform of
1,
0≤t<2,
-2t+1,
2≤t<3,
f(t) =
3t,
t-1,
3≤t 5,
t≥ 5
Q4: Find the Fourier series corresponding to the function
0
-5
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Subject :Engineering Analysis
Time: 80 min
Date:11-12-2022
Automobile Department
2nd month exam / 1" semester (2022-2023)
Note: Answer all questions,all questions have same degree.
کورس اول
شعر 3
Q1/: Use a Power series to solve the differential equation:
y" - xy = 0
Q2/:Evaluate using Cauchy's residue theorem,
sinnz²+cosz²
dz, where C is z = 3
(z-1)(z-2)
Q3/:Evaluate
dz
(z²+4)2
Where C is the circle /z-i/-2,using Cauchy's residue theorem.
Examiner: Dr. Wisam N. Hassan
Ministry of Higher Education &
Scientific Research
Babylon University
College of Engineering -
Al musayab
Subject :Engineering Analysis
Time: 80 min
Date:11-12-2022
Automobile Department
2nd month exam / 1" semester (2022-2023)
Note: Answer all questions,all questions have same degree.
کورس اول
شعر 3
Q1/: Use a Power series to solve the differential equation:
y" - xy = 0
Q2/:Evaluate using Cauchy's residue theorem,
sinnz²+cosz²
dz, where C is z = 3
(z-1)(z-2)
Q3/:Evaluate
dz
(z²+4)2
Where C is the circle /z-i/-2,using Cauchy's residue theorem.
Examiner: Dr. Wisam N. Hassan
Elementary Statistics: Picturing the World (7th Edition)
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