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प्रश्न
Expand `2x^3+7x^2+x-6` in powers of (x-2)
बेरीज
उत्तर
Let `f(x)=2x^3+7x 62+x-6` and a = 2
∴ f'(x) = 6x2+14x+1, f''(x)=12x+14, f'''(x)=12
∴ f(2) = 45, f’(2) = 53, f’’(2) = 38, f’’’(2) = 12.
Now, f(x) = f(a) + f(x-a)f’(a) +`(x-a)^2/(2!)`f''(a) +................
∴ f(x) = f(2) + (x - 2)f’(2) + `(x-2^2)/(2!)`f''(2) +.................
`2x^3+7x^2+x-6=45+(x-2)53+(x-2)^(2.19)+(x-2)^(3.2)`
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