MTH213
If \(\\mu\) is the mean operator, \ (\\mu^{2}=\)
Answer: \\(1 +\\frac{\\delta^{2}}{4}\\)
To find the solution vector \(x\) using the Gauss elimination method number of operations are required.
Answer: W(\\frac{nA{3}K6}+nA{2H\frac{nK4}\\)
Find the smallest positive root of \(2x\\ {\\mathrm{tan}x\\ }\\ =\\ 0\) by Newton- Raphson method, correct to 5 decimal places.
Answer: 1.165561
Evaluate the differences \(\\nablaA{3} [a_{3}xA{3}+a_{2}xA{2}+a_{1 }x\\ +\\ a_{0}]\).
Answer: \\(a_{3}3!hA{2}\\)
If \(P_{n}\\left(x\\right)\) is a polynomial of degree n with leadingcoefficient an, and \ (x_{0}\) is an arbitrary point, then \ (Wmath rm{\\Delta}A{n+1 }P_{n+1 }(x_{0})\\ =\)
Answer: \\(0\\)
Evaluate \(\\left|\\begin{array}{ccc}3 & 3 & 2\\\\2 & -3 & -1WW1 & 4 &1 \\end{array}\\right|\)
Answer: 16
The Taylor series expansion of is \(x-\\frac{xA{2}}{2}+\\frac{xA{3}K3}-\\frac{xA{4}K4}+\\dots\)J
Answer: \\(\\mathrm{ln}\\left(1 +x\\right)\\)
If \(\\mu\) is the mean operator and \(\\delta\) is the central difference then, \ (\\mu\\delta=\)
Answer: \\(\\frac{1}{2}\\left(\\mathrm{\\delta}\\mathrm{+}\\mathrm{\\na
The Taylor series expansion of is \(1 +x+xA{2}+xA{3}+\\dots\),
Answer: \\(\\frac{1 }{1 -x}\\)
Find an approximate value of \(\\sqrt[3]{26}\) using the mean value theorem.
Answer: 2.963
Find the eigenvalues of the matrix \ (\\left[\\begin{arrayXccc} 1 & 0 & OWW 0 & 2 & OUW 0 & 0 & 3 \\end{array}\\right]\)
Answer: \\(\\left(1,2,3\\right)\\)
If \(a=\\left(\\begin{arrayKccc}1 & 2 & 6\\\\2 & 4 & 1WW7 & 3 & 2 \\end{array}\\right)\), find \ (\\mathrm{det}\\left(A\\right)\\ \)
Answer: -13
If \(f(x)\\ =\\ xA{3}\), find the value of \(f[a,\\ b,W c]\)
Answer: a+b+c
The formula \(x_{n+1}=\\frac{x_{n- 1 }f\\left(x_{n}\\right)-x_{n}f\\left(x_{n- 1 }\\right)Kt\\left(x_{n}\\right)-t\\left(x_{n- 1}\\right)}\)is called method.
Answer: secant
Supposed that the product two matrices A and B is equal to an identity matrix, then matrix Bis of A
Answer: inverse
If \(a=AA{T}\)the \(a\) is called matrix
Answer: symmetric
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