What is taylor 5ln(x^2),x=1 ?

The answer to taylor 5ln(x^2),x=1 is 10(x-1)-5(x-1)^2+10/3 (x-1)^3-5/2 (x-1)^4+2(x-1)^5+\ldots

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taylor 5ln(x^2),x=1

taylor

5 ln (x^{2}), x = 1

10 (x - 1) - 5 (x - 1)^{2} + \frac{10}{3} (x - 1)^{3} - \frac{5}{2} (x - 1)^{4} + 2 (x - 1)^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( 5 ln ( x ^{2} ) ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( 5 ln ( x ^{2} ) ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( 5 ln ( x ^{2} ) ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 0 + \frac{10}{1 !} (x - 1) + \frac{- 10}{2 !} (x - 1)^{2} + \frac{20}{3 !} (x - 1)^{3} + \frac{- 60}{4 !} (x - 1)^{4} + \frac{240}{5 !} (x - 1)^{5} + \dots

Refine

= 10 (x - 1) - 5 (x - 1)^{2} + \frac{10}{3} (x - 1)^{3} - \frac{5}{2} (x - 1)^{4} + 2 (x - 1)^{5} + \dots

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What is taylor 5ln(x^2),x=1 ?
The answer to taylor 5ln(x^2),x=1 is 10(x-1)-5(x-1)^2+10/3 (x-1)^3-5/2 (x-1)^4+2(x-1)^5+\ldots