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9
votes
1
answer
17k
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1
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By using De Moivre's theorem,express $ \dfrac{sin7\theta}{sin\theta}$ in terms of powers of $sin\theta$ only.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
answer
1.2k
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1
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Find the external of $\int\limits_{x_{1}}^{x_{2}} (16y^2 - (y^n)^2 + x^2)dx$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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13k
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1
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Expand $cos^7 \theta$ in a series of cosines of multiple of $\theta$.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
19
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1
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16k
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1
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Using De-Moivre's theorem, prove that $ \dfrac{sin6\theta}{sin2\theta} \;=\; 16cos^4\theta-16cos^2\theta+3$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.2k
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1
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Find the curve y = f(x) for which $\int\limits_{x_{1}}^{x_{2}} (y \sqrt{1 + (y')^2}dx$ is minimum subject to the constraint $\int\limits_{x_{1}}^{x_{2}} (\sqrt{1 + (y')^2})dx = l$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.2k
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1
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Find the extremal of $$\int\frac{\sqrt{1 + (y')^2}}{x}dx$$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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2.8k
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1
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Find the curve on which the functional $\int\limits_{0}^{1} [(y')^2 + 12xy]dx$ with y(0) = 0 & y(1) = 1 can be extremised.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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5.1k
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1
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Using Rayleigh - Ritz method find an approximate solution for the extremal of the functional $l(y) = \int\limits_{0}^{1} (y^2 - 2y - 2xy)dx$ subject to y(0) = 2 y(1) = 1
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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954
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1
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Find the extremal of $\int\limits_{x_{1}}^{x_{2}} (y^2 - y^12 - 2ycoshx)dx$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.7k
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1
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Solve the boundary value problem $\int\limits_{0}^{1} (2xy + y^2 - y^{12})dx, 0 \leq x \leq 1$ y(0) = 0 y(1) = 9 by Rayleigh - Ritz method.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
2
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1
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15k
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1
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Expand $ cos^7\theta$ in a series of cosines of multiples of $\theta $.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
2
votes
1
answer
10k
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1
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Expand $ sin^7\theta$ in a series of cosines of multiples of $\theta $.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
6
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1
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5.7k
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1
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If $ sin^4\theta cos^3 \theta \;=\; acos\theta + b cos3\theta + c cos 5 \theta + d cos7 \theta \; \; \; Find \; a,b,c,d. $
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.2k
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1
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Show that $\int\limits_{0}^{2\pi} \frac{sin^2 \theta}{a + bcos\theta}d\theta = \frac{2\pi}{b^2} (a - \sqrt{a^2 - b^2}), 0 < b < a.$
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.2k
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1
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Show that the set W = {(1,x) | x $\in$ R } is a subspace of $R^2$ under operations [1,x] + [1,y] = [1, x+y]; k[1,x] = [1,kx]; k is any scalar.
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.3k
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1
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Is the set W = {[a, i, 1] | a $\in$ R} a subspace of $R^3$ under the usual addition and scalar multiplication?
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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2.3k
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1
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Find the unit vector orthogonal to both [1,1,0] & [0,1,1]
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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1.2k
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1
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Find the vector orthogonal to both [-6,4,2] and [3,1,5]
engineering mathematics updated 3.9 years ago by krithikkm200 • 10
0
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1
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8.2k
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1
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Reduce the quadratic form $Q = x^2 + y^2 + 2z^2 - 4xy - 2yz + 10xz$ to Canonical form using congruent transformation.
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
0
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1
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1.1k
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1
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If $\lambda$ is an eigen value of the matrix A with corresponding Eigen vector X, prove that $\lambda^n$ is an Eigen value of $A^n$ with corresponding Eigen vector X.
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
0
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1
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20k
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1
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Reduce the following Quadratic form $Q = 3x_{1}^2 + 5x_{2}^2 + 3x_{3}^2 - 2x_{1}x_{2} - 2x_{2} x_{3} + 2x_{3} x_{1}$ into Canonical form. Hence find its rank, index and signature.
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
0
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1
answer
2.4k
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1
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Show that matrix $A = \begin{bmatrix} 5 & -6 & -6 \\ -1 & 4 & 2 \\ 3 & -6 & -4 \end{bmatrix}$ is derogatory
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
0
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1
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1.2k
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1
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Show that the following matrix $A = \begin{bmatrix} 6 & -2 & -2 \\ -2 & 3 & -1 \\ 2 & -1 & 3 \end{bmatrix}$ is diagonalizable. Also find the diagonal form and a diagonalising matrix.
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
0
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2
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2.9k
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2
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Verify Caylay - Hamilton theorem for the matrix A and hence find $A^{-1}$ and A'.
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
0
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1
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1.3k
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1
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If $A = \begin{bmatrix} \frac{3}{2} & \frac{1}{2} \\ \frac{1}{2} & \frac{3}{2} \end{bmatrix}$ then find $e^A$ and $4^A$ with the help of Modal matrix.
engineering mathematics updated 3.9 years ago by phenjoisilab • 0
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