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433
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1
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Evaluate the following: \[\lim_{x\rightarrow 1}\dfrac{x^x-x}{x-1-logx}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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384
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1
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If the following expression is true, \[ u=\dfrac{x+y}{1-xy} \ \ , \ v = tan^{-1}x + tna^{-1}y \\ Find \ \ \dfrac{\partial (u,v)}{\partial (x,y)}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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8.6k
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Show that every square matrix can be uniquely expressed as P+iQ where P and Q are Hermitian Matrices.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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423
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Find nth order derivative of \[y= \dfrac{x^2+4}{(2x+3)(x-1)^2}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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13k
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Find the extreme values of the function \[x^3+3xy^2+72x-15x^2-15y^2\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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384
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Show that \[ \lim_{x\rightarrow\infty}\left( \frac{1^{1/x}+2^{1/x}+3^{1/x}+4^{1/x} }{4}\right)^{4x}=24 \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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869
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Obtain half-range cosine series for f(x)=x(2-x) in 0
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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670
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Show that \[ J_{\frac{5}{2}}=\ \sqrt{\frac{2}{\pi{}x}} \left[\frac{3-x^2}{x^2}\sin{x-\frac{3}{x}\cos{x\ }}\right] \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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588
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Find the constant a,b,c so that \[\bar{F}=\left(x+2y+az\right)\hat{i}+\left(bx-3y-z\right)\hat{j}+(4x+\left(y+2z\right)\hat{k}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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1.3k
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Prove that the angle between two surface x2+y2+z2=9 and x2+y2-z=3 at the point (2,-1,2) is \[{\cos}^{-1}{\left(\frac{8}{3\sqrt{21}}\right)}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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3.1k
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Show that under the transformation w= 5-4z/4z-2 the circle |z|=1 in the z plane is transformed into a circle of unity in w-plane.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
0
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399
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1
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Find z transformation of { ak sin ak}, k ? 0. where a is constant
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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380
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1
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\[A=\frac{1}{7}\ \left[\begin{array}{ccc}2 & 6 & 3 \\6 & -3 & 2 \\3 & 2 & -6\end{array}\right]\] Show that- (i) |A| = 1 (ii) .adj A=A'
engineering mathematics updated 4.4 years ago by pg1118329 • 0
0
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807
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1
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Show that the Fourier cosine transform of- \[f\left(x\right)=\ \frac{1}{\sqrt{x}}\ is\ \frac{1}{\sqrt{s}}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Investigate for what value of ? and ? the equations. x+2y+3z=4, x+3y+4z=5, x+3y+?z= ? have (I) no solution (II) a unique solution (III) an infinite no. of solutions.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
1
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1
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1.1k
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1
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Obtain half range cosine series for f(x)=sin(?x/l) in 0
engineering mathematics updated 4.4 years ago by pg1118329 • 0
0
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1
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522
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1
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Show that under the transformation \[ w= \dfrac {5-4Z}{4z-2}\] the circle |z|=1 in the z-plane is transformed into a circle of unity in the w-plane. Also find the center of the circle
engineering mathematics updated 4.4 years ago by pg1118329 • 0
0
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335
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Find L.T. of \[f\left(t\right)=\ f\left(x\right)= \Bigg\{\begin{align*}{}1,\ \ \ \ \ 0<t<a \\-1,\ \ \ \ a<t<2a\end{align*} \] And f(t) = f(t+2a)
engineering mathematics updated 4.4 years ago by pg1118329 • 0
0
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431
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1
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Find the relation of linear dependence amongst the rows of the matrix \[A=\left[\begin{array}{ccc}1 & 1 & -1 & 1 \\1 & -1 & 2 & -1 \\3 & 1 & 0 & 1\end{array}\right]\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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1
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499
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1
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Solve by using L.T. \[ \dfrac {dy}{dt}+2y+\int^{t}_{0}y \ dt=\sin t \ when \ y \ (0)=1\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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488
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1
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\[ Find L \ \left\{\frac{1-cost}{t^2}\right\} \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
4
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9.0k
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Find : - L(sin2t cost cosh2t)
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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448
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1
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Evaluate \[\int_0^{\infty{}}e^{-2t}\sinh{t\frac{\sin t}{t}}\ dt\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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1
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3.3k
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Using Fourier Cosine integral prove that \[e^{-x}\cos{x=\frac{2}{\pi{}}\\int_0^{\infty{}}\frac{\left({\omega{}}^2+2\right)}{\left({\omega{}}^4+4\right)}.\\cos{\omega{}\ x\ d\omega{}}}\]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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462
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"Find the domain response using graphical & partial fraction method & prove that results are matching \[F \left(S\right)=\frac{3s}{\left(s+6\right)\left(s+2\right)}\]"
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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