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1
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7.3k
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Expand \[ f(x)=x^4-3x^2+2x^2-x+1 \] in power of (x-3).
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Test the convergence of \[\sum\frac{2^n+1}{3^n+n}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Examine the function f(x,y) = y2 + 4xy + 3x2 + x3 for extreme values.
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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519
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Show the following: \[tan^{-1}i{\displaystyle{ \Big(\dfrac{x-a}{x+a}}\Big)} = \dfrac{i}{2}log{\Big(\dfrac{x}{a}\Big)}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Separate into real and imaginary parts cos-1(3i/4).
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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3.6k
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Evaluate the following: \[ \displaystyle \lim_{x\ \to \ 0} \ \dfrac{e^x sinx-x-x^2}{x^2+xlog(1-x)}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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577
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Obtain the half range cosine series for \[\begin {align*} f(x)&=x, 0
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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933
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Find the Bi-linear Transformation which maps the points 1,i,-1 of z plane onto i,0,-i of w-plane
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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8.0k
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Show that the transformation \( w=\dfrac{i-iz}{1+z} \) maps the unit circle |z|=1 into real axis of w plane.
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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706
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\[ \text {Evaluate }\int^\infty_0 e^{-t} \left ( \dfrac {\cos 3t - \cos 2t}{t} \right )dt \]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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3.8k
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Find the value of 'p' such that the function \[ f(x)=\dfrac {1}{2} \log (x^2 + y^2)+t\tan^{-1}\left ( \dfrac {py}{x} \right )\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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564
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Find \[ i) \ L^{-1} \left [ \dfrac {2s-1}{s^2 + 4s + 29} \right ] \\ii) \ \L^{-1} \left [ \cot ^{-1} \left ( \dfrac {s+3}{2} \right ) \right ] \]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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500
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Obtain half range sine series for \[ \begin {align*} f(x) & = x, 0\le x \le 2 \\ &=4-x, 2\le x \le 4 \end{align*} \]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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503
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Evaluate \[\int_0^{\infty{}}\frac{\left(\cos{6t-cos4t}\right)}{t}\ dt\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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433
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Obtain half range sine series for f(x)=x2 in 0
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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606
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Find the half range sine series for f(x) = ?x - x2 in [ 0, ? ]. Hence find \[\sum_{n=1}^{\infty{}}\frac{1}{{(\ 2n-1)}^6}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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574
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Show that \[\int_0^{\infty{}}\frac{\sin{2t+\sin{3t}}}{te^t}dt=\ \frac{3\pi{}}{4}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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651
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Show that \[L(cos\ at\ cosh\ at)=\frac{s^3}{s^4+\ 4a^4}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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448
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Obtain half-range sine series for f(x)= x (2-x) in 0
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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4.3k
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Determine whether following functions are positive real. \[ (i)\ \dfrac {s(s+3)(s+5)}{(s+1)(s+4)} \\(ii)\ \dfrac {2s^2+2s+4}{(s+1)(s^2+2)}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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The equations of two lines of Regression are 3x + 2y = 26 , 6x + y = 31 Find
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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1.0k
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Method steepest descent
engineering mathematics updated 4.6 years ago by 19bcs3866 • 10
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530
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Express the matrix \( A =\begin{bmatrix}1 & 0& 5& 3\\-2& 1& 6& 1\\3 & 2& 7& 1\\4& -4& 2& 0\end{bmatrix} \) as the sum of symmetric and skew- symmetric matrices.
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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506
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If \(u = x^2+y^2+z^2 \)/, where \( x = e^t, y = e^t \sin t, z = e^t \cos t \)/ Prove that \[\frac{du}{dt} = 4e^{2t}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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1.1k
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Show that \[\sin \left ( e^x -1 \right ) = x+\frac{x^2}{2}-\frac{5x^4}{24}+.........\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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