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tangent f(x)=e^{x/3}

解答

切线

f (x) = e^{\frac{x}{3}}

解答

y = e^{\frac{a _{0}}{3}} \frac{1}{3} x + e^{\frac{a _{0}}{3}} - e^{\frac{a _{0}}{3}} \frac{1}{3} a_{0}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, e^{\frac{a _{0}}{3}})

计算

f (x) = e^{\frac{x}{3}}

的斜率:

\frac{df ( x )}{d x} = e^{\frac{x}{3}} \frac{1}{3}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = e^{\frac{a _{0}}{3}} \frac{1}{3}

找到斜率 m=

e^{\frac{a _{0}}{3}} \frac{1}{3}

且穿过

(a_{0}, e^{\frac{a _{0}}{3}})

的直线:

y = e^{\frac{a _{0}}{3}} \frac{1}{3} x + e^{\frac{a _{0}}{3}} - e^{\frac{a _{0}}{3}} \frac{1}{3} a_{0}

y = e^{\frac{a _{0}}{3}} \frac{1}{3} x + e^{\frac{a _{0}}{3}} - e^{\frac{a _{0}}{3}} \frac{1}{3} a_{0}

作图

流行的例子

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\int x e^{\frac{1}{2} x} d x

tangent 2x^4+(3x)/5

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integral of cos((2pinx)/3)

\int cos (\frac{2 πn x}{3}) d x

(d^2)/(dx^2)(21e^{1/x})

\frac{d ^{2}}{d x ^{2}} (21 e^{\frac{1}{x}})

limit as x approaches infinity of (1-2/x)^{x+3}

x \to \infty lim ((1 - \frac{2}{x})^{x + 3})