What is taylor-(x-3)^3,1 ?

The answer to taylor-(x-3)^3,1 is 8-12(x-1)+6(x-1)^2-(x-1)^3

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taylor-(x-3)^3,1

taylor

- (x - 3)^{3}, 1

8 - 12 (x - 1) + 6 (x - 1)^{2} - (x - 1)^{3}

Solution steps

Apply the Taylor Formula

= 8 + \frac{\frac{d}{d x} ( - ( x - 3 ) ^{3} ) ( 1 )}{1 !} (x - 1) + \frac{\frac{d ^{2}}{d x ^{2}} ( - ( x - 3 ) ^{3} ) ( 1 )}{2 !} (x - 1)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( - ( x - 3 ) ^{3} ) ( 1 )}{3 !} (x - 1)^{3} + \dots

Evaluate Derivatives

= 8 + \frac{- 12}{1 !} (x - 1) + \frac{12}{2 !} (x - 1)^{2} + \frac{- 6}{3 !} (x - 1)^{3} + \frac{0}{4 !} (x - 1)^{4} + \frac{0}{5 !} (x - 1)^{5} + \frac{0}{6 !} (x - 1)^{6} + \frac{0}{7 !} (x - 1)^{7} + \frac{0}{8 !} (x - 1)^{8} + \frac{0}{9 !} (x - 1)^{9} + \frac{0}{10 !} (x - 1)^{10}

Refine

= 8 - 12 (x - 1) + 6 (x - 1)^{2} - (x - 1)^{3}

h \to 0 lim \frac{( ( 1 + h ) e ^{(1 + h)^{2}} - 3 )}{h}

f (x) = 5 x^{3}

\int - \frac{cos ( 3 x )}{3} d x

\int \frac{0.25}{( 0.2 5 ^{2} + x ^{2} ) ^{\frac{3}{2}}} d x

x \to 0 lim (\frac{4 x ^{2}}{x ^{2}})

What is taylor-(x-3)^3,1 ?
The answer to taylor-(x-3)^3,1 is 8-12(x-1)+6(x-1)^2-(x-1)^3