please help **Taylor Series Expansion of Function \( x^{0.3} \)****Problem Statement:** Find the first four terms of the Taylor series for the function \( x^{0.3} \) about the point \( a = 8 \). Your answers should include the variable \( x \) when appropriate.**Solution:** The Taylor series expansion for the function \( x^{0.3} \) around the point \( a = 8 \) is given by:\[ x^{0.3} = 1.86606 + 0.06977(x - 8) + (-0.00306)(x - 8)^2 + 0.00021(x - 8)^3 + \ldots \]This expansion is calculated by evaluating the derivatives of \( x^{0.3} \) at the point \( x = 8 \) and constructing the series by applying the Taylor series formula:\[f(x) \approx f(a) + f'(a)(x - a) + \frac{f''(a)}{2!}(x - a)^2 + \frac{f'''(a)}{3!}(x - a)^3 + \ldots\]Where:- \( f(a) = 1.86606 \)- \( f'(a) \approx 0.06977 \)- \( f''(a) \approx -0.00306 \)- \( f'''(a)/3! \approx 0.00021 \)These terms are each represented with the corresponding variable components \( (x - 8)^n \) for each degree \( n \) of the expansion.

Name: please help **Taylor Series Expansion of Function \( x^{0.3} \)****Pro
Uploaded: 2024-03-20T07:07:37.000Z
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Description: please help **Taylor Series Expansion of Function \( x^{0.3} \)****Problem Statement:** Find the first four terms of the Taylor series for the function \( x^{0.3} \) about the point \( a = 8 \). Your answers should include the variable \( x \) when