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E qxxg o. May 29, 18Transcript Ex23, 5 Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i) deg p(x) = deg q(x) Introduction Ex23, 5 Give examples of polynomial p(x), g(x), q(x) and r(x), which satisfy the division algorithm and (i) deg p(x) = deg q(x) We have to find p(x), g(x), q(x) &. Tov Kóapo n RETTí6a 61aaxí<El aáPKa an' tov Kpatripa Iwvíaç. '' }vvP vUE Z ov.

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ê$ �0 9 1 1. The rational function f(x) = P(x) / Q(x) in lowest terms has an oblique asymptote if the degree of the numerator, P(x), is exactly one greater than the degree of the denominator, Q(x) You can find oblique asymptotes using polynomial division, where the quotient is. 2 0r b K10 s 8 £.

I q $ ±. Big O notation is a mathematical notation that describes the limiting behavior of a function when the argument tends towards a particular value or infinity Big O is a member of a family of notations invented by Paul Bachmann, Edmund Landau, and others, collectively called Bachmann–Landau notation or asymptotic notation In computer science, big O notation is used to classify. G 2 x µ.

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A q $ ±. Nowp= q =) kfkp = kfkq andwearedonetrivially,soletp<q We would like to use H older with g(x) = 1 and some conjugate exponents 6 Real Analysis Qual Seminar , with 1 1 = 1 Ansatz Let = q p and = q q p, so 1 1 = p q q p q = q q = 1 Now use H older with f= fp to get kfpgk 1 kfpk kgk (I2) Now remembering that g= 1, we have kfpgk. @ h k p / q m % j ' g q m e ».

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62 z, h 126 z 8 5 ý. P H 8 Ù. For f(x) = px q and g(x) = 1/ (xq), pnotequalto 0, find (f o g) (x) and (g o f)(x) Then determine whether (f o x) (x) = (f o g)(x) = g o f) (x).

D l vP XsXU u îõõUõóíï. Wux\ Åq wk Õqj ³wuqk ojqj. The Qfunction is well tabulated and can be computed directly in most of the mathematical software packages such as R and those available in Python, MATLAB and Mathematica Some values of the Qfunction are given below for reference Q(00) 1/000 Q(01) 1/ Q(02) 1/.

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X k z °. Composite functions and Evaluating functions f(x), g(x), fog(x), gof(x) Calculator 1 f(x)=2x1, g(x)=x5, Find fog(x) 2 fog(x)=(x2)/(3x), f(x)=x2, Find gof(x. ³(Table 1) 8 x Þ.

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