mca1030 smu mca Winter 2014 Ist sem assignment

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Winter 2014

PROGRAM	MCA(REVISED FALL 2012)
SEMESTER	FIRST
SUBJECT CODE & NAME	MCA1030- FOUNDATION OF MATHEMATICS
CREDIT	4
BK ID	B1646
MAX. MARKS	60

Q1. State Leibnitz’s theorem. Find the n^th derivative of(𝑥)= 𝑥²𝑒^𝑎𝑥, using Leibnitz theorem. [2+8] 10

Answer.

Leibnitz’s theorem

Q2. Define Tautology and contradiction. Show that

a) (pV q) V (~ p) is a tautology.

b) (p^ q) ^ (~ p) is a contradiction [2+2+3+3] 10 marks

Answer.

Q3. State Lagrange’s Theorem. Verify Lagrange’s mean value theorem for the function f(x) = 3 x² – 5x + 1 defined in interval [2, 5] [2+8] 10 marks

Answer.

Lagrange’s Theorem

Let f: [a,b] ->R be a continuous function such that f: (a,b)->R is differentiable. Then, there exists c ε (a,b) such that [f(b)-f(a)]/(b-a)  =f’(c).

Q4. 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. [2+8] 10 marks

Answer.

Negation

An assertion that a statement fails or denial of a statement is called the negation of the statement. The negation of a statement is generally formed by introducing the word “not” at some proper place in the statement or by prefixing the statement with “It is not the case that” or “It is false that”. The negation of a

Q5. Find the asymptote parallel to the coordinate axis of the following curves

(i) (𝑥²+𝑦²)x−𝑎𝑦²=0

(ii) 𝑥²𝑦²−𝑎²(𝑥²+𝑦²)=0 [5+5] 10 marks

Answer.

Solution: (i) We have  (𝑥²+𝑦²)x−𝑎𝑦²=0

Or  x³+(x-a)y²=0

Q6. Define (i) Set (ii) Null Set (iii) Subset (iv) Power set (v) Union set [5*2] 10 marks

Answer.

(i)            Set

A set is a well defined collection of objects. The following points may be noted:

i) Objects, elements and members of a set are synonymous terms.

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