Dear students get fully solved SMU MBA Spring 2014 assignments
Send your semester &
Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
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ASSIGNMENT
|
PROGRAM
|
MCA(REVISED
FALL 2012)
|
|
SEMESTER
|
FIRST
|
|
SUBJECT CODE
& NAME
|
MCA1030-
FOUNDATION OF MATHEMATICS
|
|
CREDIT
|
4
|
|
BK ID
|
B1646
|
|
MAX.MARKS
|
60
|
Note:
Answer all questions. Kindly note that answers for 10 marks questions should be
approximately of 400 words. Each question is followed by evaluation scheme.
Q.1 State
Leibnitz’s theorem. Find the nth derivative of𝑦(𝑥)= 𝑥2𝑒𝑎𝑥, using Leibnitz theorem.
Answer:
- Leibniz's rule for differentiation under the
integral sign, named after Gottfried Leibniz, tells us that if we have an
integral of the form
Then for x in (x0, x1) the derivative of
this integral is thus expressible
Provided that f and its partial derivative
f(x) are both continuous over a region in the form [x0, x1] × [y0, y1].Thus
under certain conditions, one may interchange the integral and partial
differential operators. This important result is particularly useful in
Q.2 Define
Tautology and contradiction. Show that
a)
(pn q) n (~ p) is a
tautology.
b)
(pÙ q) Ù(~ p) is a
contradiction
Answer: - Tautology: - A proposition which is always true is called a
tautology. The column of a tautology in a truth table contains only T's. For
example, if is a proposition, then is a tautology. We could have used
tautologies for proving all the previous laws; just add an extra column to each
truth table, corresponding to the specific logical equivalence and check that
this column
Q.3 State Lagrange’s Theorem. Verify Lagrange’s mean value theorem for
the function
f(x) = 3 x2 – 5x + 1 defined in interval [2, 5]
Answer: - Suppose f is a
function defined on a closed interval [a,b] (with a<b ) such that the
following two conditions hold:
Q.4 Define Negation. Write the negation of each of the following
conjunctions:
A) Paris is in France and London is in England.
B) 2 + 3 = 5 and 8 < 10.
Answer: - Negation: - The action
or logical operation of negating or making negative b : a negative statement, judgment, or doctrine;
especially : a logical proposition
formed by asserting the falsity of a given proposition .
·
Negation refers
to contradiction and not to a contrary statement.
·
We should
be very careful while writing
·
·
·
Q.5 Find
the asymptote parallel to the coordinate axis of the following curves
(i) (𝑥2+𝑦2)𝑥−𝑎𝑦2=0
(ii) 𝑥2𝑦2−𝑎2(𝑥2+𝑦2)=0
Answer: -
(I) (𝑥2+𝑦2)𝑥−𝑎𝑦2=0
F(x) = (𝑥2+𝑦2)𝑥−𝑎𝑦2
(b
)𝑥2𝑦2−𝑎2(𝑥2+𝑦2)=0
Q.6 Define (I) Set (ii) Null Set (iii) Subset (iv) Power set (v)Union
set
Answer: - Set: - In everyday
life, we have to deal with the collections of objects of one kind or the other.
·
The collection
of even natural numbers less than 12 i.e., of the numbers 2,4,6,8, and 10.
·
The
collection of vowels in the English alphabet, i.e., of the letters a ,e ,i ,o ,
u.
·
The
collection of all students of class MCA 1st semester of your college.
·
In each of
the above collections, it is
Dear students get fully solved SMU MBA Spring 2014 assignments
Send your semester &
Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601
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