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show that \[ \tan^{-1} \left ( \dfrac {x+iy}{x-iy} \right ) = \dfrac {\pi}{4} + \dfrac {i}{2}\log \left ( \dfrac {x+y}{x-y} \right ) \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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If y=sinθ+cos θ then prove that \[y_n = r^n \sqrt{1+(-1)^n \sin 2 \theta} \] where θ rx
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Prove that \[ \log \sec x=\dfrac {x^2}{2}+ \dfrac {x^4}{12}+ \dfrac {x^6}{45}+ \cdots \ \cdots \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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If y = etan-1x prove that (1+x2)yn+2+[2 (n+1) x-1]yn+1+n (n+1)yn = 0
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Prove that ( cos^6 heta+sin^6 heta=dfrac{1}{8}[3cos 4 heta+5] )
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Solve the system of equation by Gauss Siedel Method. 2x - 4y + 49z = 49 43x + 2y + 25z = 23 3x + 53y + 3z = 91
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Solve the system of equation by Gauss Jordan Method x + 2y + 6z = 22, 3x + 4y + z = 26, 6x - y - z = 19
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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State an prove Euler's theorem for a homogeneous function in two variables.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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find the rank of the Matrix by reducing it to normal form. [egin{bmatrix} 1 & 1 & 1\ 1 & -1 & -1\ 3 & 1 & 1 end{bmatrix}]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Using De Moivre's theorem prove that \[\cos ^6\theta -\sin ^6\theta =\frac{1}{16}\left ( \cos 6\theta +15\cos 2\theta \right )\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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If \( y = \left ( x+\sqrt{x^2-1} \right )^m \)/, Prove That \[\left ( x^2-1 \right )y_{n+2}+(2n+1)xy_{n+1}+\left ( n^2-m^2 \right ) y _n =0\].
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Solve the following system of equations by Gauss-Seidel Iterative Method upto four interations. 4x-2y-z=40 x-6y+2z=-28 x-2y+12z = -86
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Using cauchy residue theorem evaluate the following integral $\oint_c \frac{e^{z}dz}{(z^{2}+\pi^2)^2} dz $ Where C is the circle $|z|=4$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using cauchy residue theorem evaluate the following integral $\int_0^{2\pi} \frac{cos2\theta}{5+4cos\theta} d\theta$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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$\int_c \frac{sin^6z}{(z-\frac{\pi}{6})^3}$ dz where c is the circle |z|=1
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Expand f(z) = $\frac{1}{z^2(z-1)(z+2)}$ about z=0 for i)|z|<1 ii)1<|z|<2 iii)|z|>2
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Show that $\int_c log z dz= 2 \pi i $ where c is the unit circle in z-plane.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Using cauchy residue theorem evaluate the following integral 1) $\int_0^{2\pi} \frac{d\theta}{5+3sin\theta}$ 2) $\int_{-\infty} ^\infty \frac {x^2}{(x^2+a^2)(x^2+b^2)}dx$ a>0,b>0
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Obtain Taylor series and two distinct laurent series expansion of f(z)=$\frac{z-1}{z^2-2z-3}$ indicating the region of convergence.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Evaluate $\oint_c \frac{e^{2z}}{ (z+1)^4} dz$ where C is the circle |z-1|=3
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Evaluate $\int_0^{1+i} z^2 dz$ along 1)the line y=x 2) the parabola x = $y^2$ is the line integral independant of the path p.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Calculate Rank correlation co-efficient for the following data \begin{array}{|c|c|c|c|} \hline X& 10 & 12 & 18&18&15&40 \\ \hline y& 12& 18&25&25&50&25 \\ \hline \end{array}
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Calculate R(pearman's rank correlation) and r(karl-pearson's) from the following data. interpret our result.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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In an examination marks obtained by students in maths ,physics and chemistry are normally distributed with mean 51,53,46 and with standard deviation 15,12,16 respctively find the probability of
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Find the m.g.f.of a Random variable ,whose probability density function is , $p(X=x) = \begin{cases} (\frac{1}{2})^x, & \ x \ = 1,\ 2, \ 3... \\ 0, & elsewhere \end{cases}$ Hence find mean & variance.
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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