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प्रश्न
Expand the polynomial f(x) = x2 – 3x + 2 in power of x – 1
उत्तर
Let f(x) = x2 – 3x + 2
f(x) = x2 – 3x + 2, f(1) = 0
f'(x) = 2x – 3, f'(1) = – 1
f”(x) = 2, f”(1) = 2
Taylor series of f(x) is
f(x) = `sum_("n" = 0)^("n" = oo) "a"_"n" (x - 1)^"n"`
Where an = `("f"^(("n"))(1))/("n"!)`
∴ The required expansion is
x2 – 3x + 2 = `0 - (1(x - 1))/(1!) + (2(x - 1)^2)/(2!)`
= – (x – 1) + (x – 1)2
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