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By using Taylor's series expand tan-1 x in positive powers of (x-1) upto first four non-zero terms.
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Determine linear dependance or independance of vectors x1=[1,3,4,2] x2==[3,-5,2,6] x=[2,-1,3,4] and if dependent find the relation between them.
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Show that every square matrix can be uniquely expressed as the sum of Hermitian matrix and a skew Hermitian matrix.
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Find the nth derivative of y =sin x sin 2x sin 3x.
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Solve the equation x6+1=0
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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\[ If \lim_{x \to 0} \dfrac {a\sin hx + b \sin x}{x^3} = \dfrac {5}{3}, \] find a and b
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Find the series expansion of log(1+x) in powers of x, Hence prove that \[logx=\left(x-1\right)-\frac{1}{2}{\left(x-1\right)}^2+\frac{1}{3}{\left(x-1\right)}^3\ .....\]
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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If 'A' is skew-symmetric matrix of odd order then prove that it is singular.
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Divide 24 into three parts such that the product of the first, square of the second & cube of the third is maximum.
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Fit a straight line to the following data with x-as independent variable. | X : | 1965 | 1966 | 1967 | 1968 | 1969 || Y : | 125 | 140 | 165 | 195 | 200 |
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Examine the linear dependence or independence of vector (1,2,-1,0), (1,3,1,3), (4,2,1,-1) & (6,1,0,-5)
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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\[ Evaluate \ \lim_{x\rightarrow 0}(1+\tan x)^{cotx} \]
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Use Taylor theorem and arrange the equaition in power of x.7+(x+2)+3(x+2)3+(x+2)4-(x+2)5
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Evaluate the following: \[\lim_{x\rightarrow 1}\dfrac{x^x-x}{x-1-logx}\]
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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Find nth order derivative of \[y= \dfrac{x^2+4}{(2x+3)(x-1)^2}\]
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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Find the extreme values of the function \[x^3+3xy^2+72x-15x^2-15y^2\]
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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Obtain half-range cosine series for f(x)=x(2-x) in 0
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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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 4.1 years ago by pg1118329 • 0
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Find z transformation of { ak sin ak}, k ? 0. where a is constant
engineering mathematics updated 4.1 years ago by pg1118329 • 0
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