MTH307 Tma Solutions

MTH307

Question: The … is a technique which is developed to reduce the sum of squares of errors in fitting the unknown function.
Answer: Least squares approach

Question: A fourth order approximation of exp(x) will be…
Answer: \\(1+x+x^2/2!+x^3/3!+x^4/4!\\)

Question: The least square straight line that provides the best fit to the curve \\( y=√x\\) over the interval [0,1] is …
Answer: \\(y=4/5 x+4/15\\)

Question: Chebyshev approximation is often referred to as …
Answer: Chebyshev polynomials

Question: Solving for x in the equation\\( x^3+x^2-2x=0\\) yields …
Answer: 2 , 0, -1

Question: A function\\( P(x)\\)of the form \\(P(x)= a_0 x+ a_1 x+ a_2 x+⋯+a_n x\\) is said to be a ___ in x.
Answer: Monomial

Question: How many non-zero coefficients has \\((2x+5)(x^2-1)\\) ?
Answer: 4

Question: If a function\\( P(x)= a_0 x+ a_1 x+ a_2 x+⋯+a_n x=0\\) then the P(x) becomes
Answer: Polynomial equation

Question: The highest power to which the variable x is raised in the expression \\( P(x)= a_0 x+ a_1 x+ a_2 x+⋯+a_n x \\)is called the
Answer: [Degree of P(x)

Question: The Taylor series for cos x is given by
Answer: \\(1+x^2/2!+x^4/4!+x^6/6!\\)

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