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受欢迎的微积分 >

tangent f(x)=(sqrt(x)+1)/(sqrt(x)+3)

解答

切线

f (x) = \frac{x + 1}{x + 3}

解答

y = \frac{1}{a _{0} ( a _{0} + 3 ) ^{2}} x + \frac{a _{0}^{2} + 3 a _{0} a _{0} - 6 a _{0} - 27 a _{0} - 27}{( a _{0} - 9 ) ( a _{0} + 3 ) ^{2}}

求解步骤

计算在一般点

x = a_{0}

的切线

找到切点:

(a_{0}, \frac{( a _{0} + 1 ) ( a _{0} - 3 )}{a _{0} - 9})

计算

f (x) = \frac{x + 1}{x + 3}

的斜率:

\frac{df ( x )}{d x} = \frac{1}{x ( x + 3 ) ^{2}}

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 = \frac{1}{a _{0} ( a _{0} + 3 ) ^{2}}

找到斜率 m=

\frac{1}{a _{0} ( a _{0} + 3 ) ^{2}}

且穿过

(a_{0}, \frac{( a _{0} + 1 ) ( a _{0} - 3 )}{a _{0} - 9})

的直线:

y = \frac{1}{a _{0} ( a _{0} + 3 ) ^{2}} x + \frac{a _{0}^{2} + 3 a _{0} a _{0} - 6 a _{0} - 27 a _{0} - 27}{( a _{0} - 9 ) ( a _{0} + 3 ) ^{2}}

y = \frac{1}{a _{0} ( a _{0} + 3 ) ^{2}} x + \frac{a _{0}^{2} + 3 a _{0} a _{0} - 6 a _{0} - 27 a _{0} - 27}{( a _{0} - 9 ) ( a _{0} + 3 ) ^{2}}

作图

流行的例子

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