# Expand 2 X 3 + 7 X 2 + X − 1 in Powers of X - 2 - Applied Mathematics 1

Sum

Expand 2x^3+7x^2+x-1 in powers of x - 2

#### Solution

Let  f(x) =2x^3+7x^2+x-1

Here a = 2

 f(x) =2x^3+7x^2+x-1 𝒇(𝟐)=𝟒𝟓 f'(x) =6x^2+14x+1 𝒇′(𝟐)=𝟓𝟑 f''(x) =12x+14 𝒇′′(𝟐)=𝟑𝟖

𝒇′′′(𝒙)=𝒇′′′(𝟐)=𝟏𝟐

Taylor’s series is :

f(x)=f(a)+(x-a)f'(a)+(x-a)^2/(2!)f''(a)+....

2x^3+7x^2+x-1=45+(x-2)53+(x-2)^2/(2!)38+(x-a)^3/(3!)12

2x^3+7x^2+x-1=45+53(x-2)+19(x-2)^2+2(x-2)^3

Concept: Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ
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