Write as a Vector Equality y=x^2 natural log of x , x^0=1/3

Problem

y=x2*ln(x),(x_0)=1/3

Solution

1. Identify the function and the point of interest. The function is ƒ(x)=x2*ln(x) and the evaluation point is (x_0)=1/3

2. Calculate the value of the function at (x_0)

ƒ(1/3)=(1/3)2*ln(1/3)

ƒ(1/3)=1/9*ln(3(−1))

ƒ(1/3)=−ln(3)/9

3. Construct the vector equality. A vector equality for a function y=ƒ(x) at a specific point (x_0) is typically represented as the vector ([x],[y]) evaluated at (x_0)

([(x_0)],[(y_0)])=([1/3],[−ln(3)/9])

Final Answer

([x],[y])=([1/3],[−ln(3)/9])

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