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vector 4
Given position vector of two points A, B and C are \[\underline a = 2i - j + k\] and \[\underline b = 2i + j + 3k\] and \[\underline c = i - 3j + k\]
i) find the distance between A and B
ii) find the angle between \[\underline a - \underline b \] and \[\underline a + \underline b...
vector 3
i) If \[F = y^2 i - 3x^2 j + yzk\], find \[\nabla XF\] and \[\nabla \bullet F\]
ii) Show that \[G = 2xy^3 i + (1 + 3x^2 y^2 )j\] is conservative vector field on the entire plane.
iii) Find a potential function \[\Phi \] so that \[\nabla \Phi = G\].
vectors 2
The electric intensity of a electrostatic function \[V(x,y,z)\] is \[E = - \nabla V\]
The elecrostatic potential produced by a unit dipole-moment, located at the origin and directed along the y-axis, is given by
\[V(x,y,z) = \frac{y}{{(x^2 + y^2 + z^2 )^{3/2} }}\]
i) Determine...
vectors
\[z = 3x^2 - 2xy + x^2 y = 2\]
i) find the vectorswhich is normal to curve at (1,1)
ii) write down a unit vector d along the line y=x and directed at the positive x direction.
iii) Find the rate of change of z in the direction of d.
Re: Higher Derivatives
thanks for the ans. but its different from mine... so can you help me find out what went wrong?
\[\lambda = 0\]
\[\lambda = 2 + 2j\sqrt 3\]
\[\lambda = 2 - 2j\sqrt 3\]
and btw how u got the exp, C1 C2 C3 ?
Re: Periodic Signals
Conclusion:
i) period is \[\frac{1}{\pi }\] , therefore it is aperiodic
ii) period is \[\frac{\pi }{2}\]
iii) period is \[\frac{1}{2}\]
funcky question
The reason is very simple. It is to connect the positive and the negative of the batteries in the shortest way. Because the circuit requires the batteries to connect in series to achieve a higher voltage.
(2What are periodic signals? How to determine if the equation is a periodic signal?
Find the fundamental period:
i) x[n] = sin(2n)
ii) x(t) = cos³(4t)
iii) \[x(t) = 1 + \sin^2(2 \pi t)\]
Find the even and odd components for each of the following signals:
i) x(t) = exp^(-2t) sin (2t)
ii) x(t) = 1 + t + t³ + t^5
iii) x(t) = 1 + sin(t) + t cos(t) + t² sin(t) cost(t)
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