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(i) Find complex form of Fourier series for f(x) = cosh3x + sinh3x in (-π,π)
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find Fourier series for f(x) = x + x2 in (-π , π) Hence deduce that \[ \dfrac{1}{1^2}+ \dfrac{1}{3^2}+ \dfrac{1}{5^2} +\frac{1}{7^2} +....= \dfrac{{\pi}^2}{8} \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find Z-transform of {k2 - 2k + 3}k ≥ 0
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the Fourier series of f(x) = cos μx in (-π,π), where μ is not an integer.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Using laplace trasnform solve the following differential equation with given condition. (D2-3D+2) y=e2t, y(0)=-3, y'(0)=5
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the analytic function f(z)=u+iv in terms of z if u-v=(x-y) (x2 + 4xy + y2)
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find inverse Laplace Transform of following (i) 2 tanh-1 s \[\left(ii\right)\frac{s^2}{\left(s^2+1\right)\left(s^2+4\right)}\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Obtain complex form of Fourier series for the functions f(x)= sin a x in (-?, ?)
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Evaluate by Green's theorem \[\int_C\bar{F}\cdot{}d\bar{r}\ where\ \ \bar{F}=xy\left(xi-yi\right) \ and \ C \ is \ r=a(1+ \cos \theta) \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find Laplace Transform of following \[\left(i\right)\ e^{-4t}\ \int_0^1u\sin{3u\ du}\] \[\left(ii\right)\ \frac{1}{t}(1-\cos{t)}\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the Fourier series expnasion for \[ f(x)= \sqrt{1-\cos x} in (0,2?) \ Hence \ deduce \ that \ \sum_{n=1}^{\infty}\dfrac{1}{4n^2 -1}=\dfrac{1}{2} \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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\[ if \ \int^{\infty}_{0}e^{-2t} \sin (t+\alpha) \cos (t-\alpha)dt=\dfrac {3}{8} \ then \ find\ \alpha \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the Laplace transform of sin t? \[H\left(t-\frac{\pi{}}{2}\right)-H\left(t-\frac{3\pi{}}{2}\right)\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the Fourier series expansion for f(x)= |sin x|, in (-?, ?)
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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If f(z)= (ax4 + bx2y2 + cy4 + dx2 - 2y2) + i(4x3y - exy3 + 4xy) is analytic, find the constants a,b,c,d,e
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the inverse z transform of \[ F\left(z\right)=\ \frac{z}{\left(z-1\right)\left(z-2\right)},\ \left\vert{}z\right\vert{}>2\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the Fourier transform of- f(x) = (1-x2), |x|<| = 0 , |x|>|, then \[f\left(s\right)=\ -2\sqrt{\frac{2}{\pi{}}}\left[\frac{scoss-sins}{s^3}\right]\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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If L[f(t)] = f(s), then prove that L[ tn f(t)] = (-1)n dn/dsn f(s), Hence find the Laplace transform of f(t) = t cos2t
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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For what value of λ the equations 3x-2y+ λ z=1, 2x+y+z=2, x+2y- λz= -1 will have no unique solution ? Will the equations have any solution for this value of λ ?
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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State Convolution theorem and hence find inverse Laplace transform of the function using the same :- \[f(s)\ =\frac{{\left(s+3\right)}^2}{{\left(s^2+6s+5\right)}^2}\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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If f(k)= 4kU(K), g(k)= 5kU(k), then find the z-transform of f(k) x g(k).
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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\[ \left.\begin{matrix} f(x)&= \pi x 0\leq x \leq 1 \\ f(x)&=\pi (2-x)1 \leq x \leq 2 \end{matrix}\right\} with \ period \ 2 \] Find the Fourier series expansion
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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600
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Reduce the matrix to normal form and find its rank :- \[\left[\begin{array}{cccc}2 & 3 & -1 & -1 \\1 & -1 & -2 & -4 \\3 & 1 & 3 & -2 \\6 & 3 & 0 & -7\end{array}\right]\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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595
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(D2- 3D+2) y=4 e21, with y(0) = -3, y'(0)=5 solve using Laplace transform.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Find the Z-transform of f(k) =ak, k≥0.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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