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Engineering Mathematics

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0
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532
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Prove the following: \[\Big [\bar b \times\bar a\ \ \ \bar a \times\bar c \ \ \ \bar a \times \bar b \Big] = \Big[ \bar a \ \ \bar b \ \ \bar c \Big]^2\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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472
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Prove the following: \[\log \ \sec \ x = \Big [ \dfrac{x^2}{2}+\dfrac{x^4}{12}+\dfrac{x^6}{45}... \Big]\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If the given function, f(xy2,z - 2x) = 0, thenprove that \[2x\dfrac{\partial z}{\partial y} -y\dfrac{\partial z}{\partial y}=4x\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If z = tan(y+ax) + (y-ax)(3/2) \[\dfrac{\partial^2z}{\partial x^2} =a^2 \dfrac{\partial^2z}{\partial y^2}\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Prove the following: x2y(n+2) + (2n+1)xy(n+1) + 2n2 yn = 0 \[if \ \ \ cos ^{-1} \Big(\dfrac{y}{b} \Big) = log\Big(\dfrac{x}{n} \Big)n\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Prove that αn + βn = 2cos n θ cosecn θ if α and β roots of the equation z2sin2 θ - z sin2θ + 1 = 0 .
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Prove that arg z1 - arg z2 = π/2 if |z1 + z2 |= |z1 - z2 | where z2 , z1 are complex numbers.
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If u=f(e(y-z),e(z-x),e(x-y)) then \[Prove \ that = \dfrac{{\partial}u}{{\partial}x}+\dfrac{{\partial}u}{{\partial}y}+\dfrac{{\partial}u}{{\partial}z} =0\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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455
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If b+ic = (1+a)z and a2 + b2 + c2 = 1 then \[Prove \ that = \dfrac{a+ib}{1+c}=\dfrac{1+iz}{1-iz} \]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Test the convergence of \[ \dfrac{x}{1.2}+\dfrac{x^2}{3.4}+\dfrac{x^3}{5.6}+\dfrac{x^4}{7.8}+......(x > 0, \ x \neq 1 ) \]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Prove that real part of \[ (1+i\sqrt{3})^{(1+l\sqrt{3})} \ is \ 2e^{-\pi/\sqrt{3}} \ \cos \left (\dfrac {\pi}{3}+\sqrt{3}\cdot \log 2 \right ) \]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Prove that tanh-1 (sinθ) = cosh-1 (secθ)
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If arg(z+1) = π/6 and arg(z-1) = 2π/3 find **z**, a complex number.
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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510
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\[ Prove\ that \ \nabla\cdot\left\{ \frac{f(r)}{r}\bar{r} \right \}= \frac{1}{r^2} \frac{d}{dr}\ [r^2f(r)] \] hence or otherwise prove that div \[\left(r^n\bar{r}\right)=\left(n+3\right)r^n\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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\[prove\ that\ \tan 7\theta =\frac{7\tan\theta -35\tan^3 \theta +21\tan^5 \theta -\tan^7\theta}{1-21\tan^2\theta+35\tan^4\theta -7\tan^6 \theta} \]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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\[if\ y=\sin \left[\log\left(x^2+2x+1\right) \right] \ then\ prove\ that\ \\\left(x+1\right)^2y_{n+2}\left(2n+1\right)\left(x+1\right)y_{n+1}+\left(n^2+4\right)y_n=0.\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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415
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\[ If\ f(x)=\frac{1}{x^2}\ and\ g(x)=\frac{1}{x}\ \] then show that c of C.M.V.T. is H.M of a & b where a>0, b>0.
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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\[ If\ z=\log{\left(x^2+y^2\right)}+\frac{x^2+y^2}{x+y}-2\log{\left(x+y\right)},\\ prove\ that\ x\frac{\partial{}z}{\partial{}x}+y\frac{\partial{}z}{\partial{}y}=\frac{x^2+y^2}{x+y}\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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500
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If \[Args\left(z+1\right)=\frac{\pi{}}{6}\ \&\ Args\left(z-1\right)=\frac{2\pi{}}{3}\ find\ z.\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If y = (sin-1x)2, obtain yn(0).
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Solve the system of linear equation by Crout's method x - y + 2z = 2; 3x + 2y - 3z = 2; 4x - 4y + 2z = 2
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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995
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Considering only the principal value, if (1 + i tanθ)(1+i tanθ) is real, prove that its value is (sec?)(sec2θ).
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If x = u+e(-v)sin u, and y = v+e(-u)cos u, \[Find \ \ \dfrac{\partial u}{\partial y}, \dfrac{\partial v}{\partial x} \ \ using \ \ Jacobian\]
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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If tan[(π/4)+iv] = reiθ show that (i) r=1 (ii) tanθ = sinh 2v (iii) tanhv = tan(θ/2)
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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Find all stationary value of x2 + 3xy - 15x2 - 15y2 + 72x.
engineering mathematics updated 5.1 years ago by teamques10 ★ 70k
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