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991
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Fit a straight line to the following data : | Year x: | 1951 | 1961 | 1971 | 1981 | 1991 || Production y: | 10 | 12 | 8 | 10 | 15 |
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Fit a second degree parabolic curve to the following data : | x : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 || y : | 2 | 6 | 7 | 8 | 10 | 11 | 11 | 10 | 9 |
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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If z=log (tan x+tan y) then prove that \[ \sin 2x \dfrac {\partial z}{\partial x} + \sin 2y \dfrac {\partial z}{\partial y} = 2 \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Discuss the maximum and minimum of f(x,y)=x3+3xy2-15(x2+y2)+72x
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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555
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Find the values of a,b & c such that \[ \lim_{x\to 0} \dfrac {a e^x - be^{-x}+cx}{x-\sin x}=4 \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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880
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Fit a straight line passing through points (0,1), (1,2), (2,3), (3,4,5), (4,6), (5,7,5).
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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\[ If \ \tan \dfrac {x}{2} = \tan h \ \dfrac {u}{2} \ then \ S.T. \\ u=\log \tan \left ( \dfrac {\pi}{4} + \dfrac {x}{2} \right ) \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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\[ If \ u = x^y \ find \ \dfrac {\partial^3 u}{\partial x \partial y \partial x} \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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If ux=yz,vy=zx, wz=xy find \[ j \left [ \dfrac {u,v,w}{x,y,z} \right ] \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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\[ If y = (x-1)^n \ then \ P.T. \ y+ \dfrac {y_1}{1!} + \dfrac{y_2}{2!}+ \dfrac {y_3}{3!}+ \cdots \ \cdots \dfrac {y_n}{n!}= x^n \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Express the matrix A as sum of Hermition and skew Hermition matrix where \[ \begin{bmatrix}3i &-1+i &3-2i \\1+i &-i &1+2i \\-3-2i &-1+2i &0\end{bmatrix} \]
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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Find the maximum and minimum values of x3+3xy2-3x2-3y2+4
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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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 4.4 years ago by pg1118329 • 0
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546
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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 4.4 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 4.4 years ago by pg1118329 • 0
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Find the nth derivative of y =sin x sin 2x sin 3x.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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442
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Solve the equation x6+1=0
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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478
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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 4.4 years ago by pg1118329 • 0
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8.9k
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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 4.4 years ago by pg1118329 • 0
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380
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If 'A' is skew-symmetric matrix of odd order then prove that it is singular.
engineering mathematics updated 4.4 years ago by pg1118329 • 0
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17k
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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 4.4 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 4.4 years ago by pg1118329 • 0
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2.6k
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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 4.4 years ago by pg1118329 • 0
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\[ Evaluate \ \lim_{x\rightarrow 0}(1+\tan x)^{cotx} \]
engineering mathematics updated 4.4 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 4.4 years ago by pg1118329 • 0
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