What is taylor f(t)=ln(1+2*t) ?

The answer to taylor f(t)=ln(1+2*t) is 2t-2t^2+8/3 t^3-4t^4+32/5 t^5+\ldots

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taylor f(t)=ln(1+2*t)

taylor

f (t) = ln (1 + 2 \cdot t)

2 t - 2 t^{2} + \frac{8}{3} t^{3} - 4 t^{4} + \frac{32}{5} t^{5} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 0 + \frac{2}{1 !} t + \frac{- 4}{2 !} t^{2} + \frac{16}{3 !} t^{3} + \frac{- 96}{4 !} t^{4} + \frac{768}{5 !} t^{5} + \dots

Refine

= 2 t - 2 t^{2} + \frac{8}{3} t^{3} - 4 t^{4} + \frac{32}{5} t^{5} + \dots

\int \frac{7}{( x - 10 ) ^{7}} d x

\int \frac{x}{3 x - 2} d x

f (x) = \frac{- x ^{2} - 1}{( x ^{2} - 1 ) ^{2}}

\int tan^{3} (19 π x) d x

\frac{1}{1 + x}

What is taylor f(t)=ln(1+2*t) ?
The answer to taylor f(t)=ln(1+2*t) is 2t-2t^2+8/3 t^3-4t^4+32/5 t^5+\ldots