ALLAMA IQBAL OPEN UNIVERSITY, ISLAMABAD
(Department of Mathematics)
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2.
WARNING
PLAGIARISM OR HIRING OF GHOST WRITER(S) FOR SOLVING
THE ASSIGNMENT(S) WILL DEBAR THE STUDENT FROM AWARD
OF DEGREE/CERTIFICATE, IF FOUND AT ANY STAGE.
SUBMITTING ASSIGNMENTS BORROWED OR STOLEN FROM
OTHER(S) AS ONE’S OWN WILL BE PENALIZED AS DEFINED IN
“AIOU PLAGIARISM POLICY”.
Course: Mathematics for Computing-II (3403)
Level: BS (Computer Science)
Semester: Spring, 2017
Total Marks: 100
Pass Marks: 50
ASSIGNMENT No. 1
(Units 1–3)
Q.1 a)
b)
Find the third Maclaurin polynomial for
Find the general term of the sequence, starting with
whether the sequence converges, and if so find its limit.
(20)
, determine
Q.2 a)
Use differentiation to show that the sequence is strictly increasing or strictly
decreasing.
(20)
b)
Classify the series as absolutely convergent, conditionally convergent, or
divergent.
Q.3 a)
b)
Q.4 a)
Find the radius of convergence and the interval of convergence.
(20)
Find the slope of the tangent line to the polar curve for the given value of .
Sketch the parabola and label the focus, vertex and directrix.
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(20)
b)
Q.5 a)
b)
Find an equation of the parabola that satisfies the given conditions.
Show that (2,1,6) , (4,7,9) and (8,5,-6) are the vertices of a right triangle. (20)
Find
and check that it is orthogonal to both
, where
ASSIGNMENT No. 2
(Units 4-7)
Total Marks: 100
Q.1 a)
b)
Q.2 a)
b)
Q.3 a)
b)
Q.4 a)
b)
Pass Marks: 50
Find the parametric equations that correspond to the given vector
equation:
(20)
Find the limit:
Find
when
Given
find
.
Use an appropriate form of the chain rule to find
(20)
.
(20)
Use polar coordinates to evaluate the double integral.
(20)
Where R is the region in the first quadrant within the circle
Evaluate the triple integral:
.
Evaluate the Integral:
Where G is the solid in the first octant that is bounded by the parabolic
cylinder
and the planes
.
Q.5 a)
b)
Find
. if
Show that the line integral
(20)
2
is independent of the path.
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