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泰勒 x^4+2x,1

解答

泰勒

x^{4} + 2 x, 1

解答

3 + 6 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

求解步骤

应用泰勒公式

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

求导数

= 3 + \frac{6}{1 !} (x - 1) + \frac{12}{2 !} (x - 1)^{2} + \frac{24}{3 !} (x - 1)^{3} + \frac{24}{4 !} (x - 1)^{4}

整理后得

= 3 + 6 (x - 1) + 6 (x - 1)^{2} + 4 (x - 1)^{3} + (x - 1)^{4}

流行的例子

(12x+x^2+0.05x^3)^'

(12 x + x^{2} + 0.05 x^{3})^{^{'}}

integral from-1 to 1 of e^y-(y^2-2)

\int_{- 1}^{1} e^{y} - (y^{2} - 2) d y

sum from n=2 to infinity of 3/(4^n)

n = 2 \sum \infty \frac{3}{4 ^{n}}

(\partial)/(\partial x)(ln(1+x^2+y^2))

\frac{\partial}{\partial x} (ln (1 + x^{2} + y^{2}))

(\partial)/(\partial x)(13.12+0.6215x-11.37y^{0.16}+0.3965xy^{0.16})

\frac{\partial}{\partial x} (13.12 + 0.6215 x - 11.37 y^{0.16} + 0.3965 x y^{0.16})