Sunday, 13 November 2016

mca113 smu mca fall 2016 (jan/feb 2017 exam) Ist sem assignment

NAME

ROLL NO.

DRIVE
FALL 2016
PROGRAM/SEMESTER
MCA SEMESTER 1
SUBJECT CODE & NAME
MCA113- FOUNDATION OF MATHEMATICS
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1 Draw the truth tables of Conjunction, disjunction and Bi-conditional statements.

Answer: Regarding truth value of conjuction of statements, We have
(D1) : TÙ T = T
(D2): TÙ F = FÙ T

2 If y = e^ax cos^3x sin^2x find dy/dx

Answer: y = eax cos3x sin2x

Dy/dx = dy/dx(eax cos3x sin2x)

Dy/dx = eax


3 Find the Taylors expansion of f(x) = Sin x at x = 0.

Answer: Taylor's Theorem is an extension of the Mean value theorem.

Though Taylor's Theorem has applications in numerical methods, inequalities and local maxima and minima, it basically deals with approximation of functions by polynomials.

4 Find the nth derivative of
i) Cos mx
ii) Cos^2x

Answer: i) Cos mx
y^(1) = - m sin mx
y^(2) = - m^2 cos mx
y^(3) = m^3 sin mx
y^(4

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