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ser-zykov [4K]
3 years ago
8

Find the smallest integer n for an O(xn) estimate of order of the function f(x)

Mathematics
1 answer:
alexdok [17]3 years ago
6 0

Answer with explanation:

f(x)=\frac{(x^3+x^2+5)(x^4-3x^2)}{(2x^2+2x-3)(4x^2+7)}\\\\f(x)=\frac{x^3\times (x^4-3x^2)+x^2 \times (x^4-3x^2)+5 \times (x^4-3x^2)}{2x^2\times (4x^2+7)+2x(4x^2+7)-3\times (4x^2+7)}\\\\f(x)=\frac{x^7-3x^5+x^6-3x^4+5x^4-15x^2}{8x^4+14x^2+8x^3+14 x-12x^2-21}\\\\f(x)=\frac{x^7+x^6-3x^5+2x^4-15x^2}{8x^4+8x^3+2x^2+14 x-21}

The largest degree of numerator is 7 , while the largest degree of denominator is 4.So, as we know

 \frac{x^a}{x^b}=x^{a-b}\\\\\frac{x^7}{x^4}=x^{7-4}\\\\=x^3

→So, order of the function is the highest degree in the function raised to power.Highest degree is 3,when you will reduce the function in Expression form.

So, Degree=3

Order=1

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