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2
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3.7k
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Show that roots of the equation (x+1)6 + (x-1)6 = 0 are given by \[-i\cot\Big[ \dfrac{(2k+1)\pi}{12} \Big] \ \ \ , \ k=0,1,2,3,4,5\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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937
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If u = log (tanx + tany) \[2x\dfrac{\partial u}{\partial x}+sin2y\dfrac{\partial u}{\partial y} = 2 \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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489
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Prove the following: \[\dfrac{1}{1- \dfrac{1}{1-\dfrac{1}{1-\cos h^2x}}} = \cos h^2 x\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Prove the following if y1/m + y-1/m = 2x; (x2 -1) y(n+2) + (2n+1)xy(n+1) + (n2-m2)yn = 0
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Using Gauss- Seidel iteration method solve, 10x1 + x2 + x3 = 12, 2x1 + 10x2 + x3=13, 2x1 + 2x2 + 10x3 = 14 Upto three iterations.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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If tan[log(x + iy)] = a+ib, \[prove \ that \ tan[log(x^2+y^2)]=\dfrac{2a}{1-a^2-b^2}\] where a2 + b2 ≠ 1.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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633
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If x = u cos v and y = u sin v \[\dfrac{\partial(x,y)}{\partial(u,v)}.\dfrac{\partial(u,v)}{\partial(x,y)} =1\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the stationary values of x3 + y3 - 3axy, a > 0
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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488
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Reduce matrix A to normal form and find its rank where \[A={ \left[ \begin{array}{ccc} 1 & 2 & 3 &2 \\ 2 & 3 & 5 & 1 \\ 1 & 3 & 4 &5 \end{array} \right]}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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If y = cos x.cos 2x.cos 3x then find its nth order derivative
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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353
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If x = r cosθ, y = r sinθ; \[ \dfrac{\partial(x,y)}{\partial(r, \theta)} \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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334
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If u = log (x2+y2), prove that \[\dfrac{\partial^2 u}{\partial x \ \partial y} = \dfrac{\partial^2 u}{\partial y \ \partial x}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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If cosh x = sec θ, prove that x = log (sec θ + tan θ)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
2
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\[If\ u=\sin{\left(x^2+y^2\right)}and\ a^2x^2+b^2y^2=c^2\ find\frac{du}{dx}.\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Solve correctly upto three iterations the following equaition by Gauss-Seidel method. 10x-5y-2z=3, 4x-10y+3z=-3, x+6y+10z=-3.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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\[ If\ y=\cos(m\sin^{-1}X)\ \\prove\ that\ \left(1-x^2 \right)y_{n+2}-\left(2n+1\right)xy_{n+1}+ \left(m^2-n^2\right)_n^y=0\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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858
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If sin4θ cos3θ = a cosθ- bcos3θ + ccos 5θ + dcos 7θ then find a,b,c,d
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Solve by Crout's Method the system of equaition 2x+3y+z=-1, 5x+y+z=9, 3x+2y+4z=11
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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467
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\[ If\ (1+i \left(\tan\alpha \right)^{(1+i\ tan\beta)} \] is real then one of the principle values is \[ \left( sec\alpha \right)^{sec^2 \beta} \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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\[ if\ ux+vy=a,\frac{u}{x}+\frac{v}{y}=1,\ show\ that \ \frac{u}{x} \left(\frac{\partial x}{\partial u}\right)_v+\frac{v}{y} \left(\frac{\partial y}{\partial v}\right)_u=0 \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the stationary values of sin x sin (x+y).
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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\[ Z^3={\left(z+1\right)}^3,\ then\ show\ that\ z=\frac{-1}{2}+\frac{i}{2}\cot{\frac{\theta{}}{2}\ where\ \theta{}=\ 20\frac{\pi{}}{3}.} \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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\[ prove\ that \log{\left(1-x+x^2\right)}=-x+\frac{x^2}{2}+\frac{2x^3}{3}\ ---- \ \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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\[If\ u=f\left(\frac{x-y}{xy},\frac{z-x}{zx}\right)prove\ that\ \ x^2\frac{\partial{}u}{\partial{}x}+y^2\frac{\partial{}u}{\partial{}y}+z^2\frac{\partial{}u}{\partial{}z}=0\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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\[ If\ y=\frac{\sin^{-1}x}{\sqrt{1-x^2}}\ \\ prove\ that\\ \left(1-x^2 \right)y_{n+2}- \left(2n+3\right)xy_{n+1}- \left(n-1\right)^2y_n=0\ \ hence\ find\ y_n \left(0\right) \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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