What is taylor x^4-x^3+2 ?

The answer to taylor x^4-x^3+2 is 2-x^3+x^4

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taylor x^4-x^3+2

taylor

x^{4} - x^{3} + 2

2 - x^{3} + x^{4}

Solution steps

Apply the Taylor Formula

= 2 + \frac{\frac{d}{d x} ( x ^{4} - x ^{3} + 2 ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( x ^{4} - x ^{3} + 2 ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( x ^{4} - x ^{3} + 2 ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 2 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{24}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{0}{10 !} x^{10}

Refine

= 2 - x^{3} + x^{4}

\frac{d}{d x} (\frac{1}{2} x^{2} e^{- 2 x})

\frac{2 x + 9}{x}

\int \frac{y ^{3}}{( 1 - 2 y ^{4} ) ^{5}} d y

\int_{0}^{1} \frac{36}{x ^{2} - 36} d x

x \to 3 lim (\frac{x - 3}{x + 4})