What is taylor (3x-2)^{3/2} ?

The answer to taylor (3x-2)^{3/2} is 1+9/2 (x-1)+27/8 (x-1)^2-27/16 (x-1)^3+243/128 (x-1)^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor (3x-2)^{3/2}

taylor

(3 x - 2)^{\frac{3}{2}}

1 + \frac{9}{2} (x - 1) + \frac{27}{8} (x - 1)^{2} - \frac{27}{16} (x - 1)^{3} + \frac{243}{128} (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{\frac{9}{2}}{1 !} (x - 1) + \frac{\frac{27}{4}}{2 !} (x - 1)^{2} + \frac{- \frac{81}{8}}{3 !} (x - 1)^{3} + \frac{\frac{729}{16}}{4 !} (x - 1)^{4} + \dots

Refine

= 1 + \frac{9}{2} (x - 1) + \frac{27}{8} (x - 1)^{2} - \frac{27}{16} (x - 1)^{3} + \frac{243}{128} (x - 1)^{4} + \dots

\frac{d}{d x} (e^{3 x} + 3 e^{3 x} x)

x \to 0 lim (- 6 x + 9)

\int_{1}^{4} (x^{2} - 4 x + 2) d x

y = 12 x sin (x)

9 x^{2} \frac{d y}{d x} = \frac{d y}{d x} + 2 x e^{- y}

What is taylor (3x-2)^{3/2} ?
The answer to taylor (3x-2)^{3/2} is 1+9/2 (x-1)+27/8 (x-1)^2-27/16 (x-1)^3+243/128 (x-1)^4+\ldots