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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