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Popular >

taylor (-5x+24)^{3/2}

Solution

taylor

(- 5 x + 24)^{\frac{3}{2}}

Solution

48 \cdot 6^{\frac{1}{2}} - 15 \cdot 6^{\frac{1}{2}} x + \frac{25 \cdot 3 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}} x^{2} + \frac{125}{768 \cdot 6 ^{\frac{1}{2}}} x^{3} + \frac{625}{49152 \cdot 6 ^{\frac{1}{2}}} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 48 \cdot 6^{\frac{1}{2}} + \frac{\frac{d}{d x} ( ( - 5 x + 24 ) ^{\frac{3}{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( - 5 x + 24 ) ^{\frac{3}{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( - 5 x + 24 ) ^{\frac{3}{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 48 \cdot 6^{\frac{1}{2}} + \frac{- 15 \cdot 6 ^{\frac{1}{2}}}{1 !} x + \frac{\frac{25 \cdot 3 ^{\frac{1}{2}}}{8 \cdot 2 ^{\frac{1}{2}}}}{2 !} x^{2} + \frac{\frac{125}{128 \cdot 6 ^{\frac{1}{2}}}}{3 !} x^{3} + \frac{\frac{625}{2048 \cdot 6 ^{\frac{1}{2}}}}{4 !} x^{4} + \dots

Refine

= 48 \cdot 6^{\frac{1}{2}} - 15 \cdot 6^{\frac{1}{2}} x + \frac{25 \cdot 3 ^{\frac{1}{2}}}{16 \cdot 2 ^{\frac{1}{2}}} x^{2} + \frac{125}{768 \cdot 6 ^{\frac{1}{2}}} x^{3} + \frac{625}{49152 \cdot 6 ^{\frac{1}{2}}} x^{4} + \dots

Popular Examples

limit as x approaches 1 of 5/(x+1)

x \to 1 lim (\frac{5}{x + 1})

area f(x)=4-(x-1)^2,(1,3)area

f (x) = 4 - (x - 1)^{2}, (1, 3)

sum from n=0 to infinity of (-x/4)^n

n = 0 \sum \infty (- \frac{x}{4})^{n}

tangent of f(x)=ln(6-9x^2+8x^4),\at x=1 tangent of

f (x) = ln (6 - 9 x^{2} + 8 x^{4}), at x = 1

integral of (r^3)/(sqrt(4-r^2))

\int \frac{r ^{3}}{4 - r ^{2}} d r

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