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受欢迎的函数 >

f(x)=(tan(x)-5)/(sec(x))

解答

f (x) = \frac{tan ( x ) - 5}{sec ( x )}

解答

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

Range : - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )} \leq f (x) \leq - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}

X 截距 : (arctan (5) + 2 πn, 0), (arctan (5) + π + 2 πn, 0), Y 截距 : (0, - 5)

Asymptotes : 无

Extreme Points : 极大值 (- arctan (\frac{1}{5}) + π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}), 极小值 (- arctan (\frac{1}{5}) + 2 π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )})

+1

间隔符号

Domain : [2 πn, \frac{π}{2} + 2 πn) \cup (\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn) \cup (\frac{3 π}{2} + 2 πn, 2 π + 2 πn)

Range : [- \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )}, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}]

求解步骤

\frac{tan ( x ) - 5}{sec ( x )}

的周期:

2 π

\frac{tan ( x ) - 5}{sec ( x )}

的定义域

: 2 πn \leq x < \frac{π}{2} + 2 πn or \frac{π}{2} + 2 πn < x < \frac{3 π}{2} + 2 πn or \frac{3 π}{2} + 2 πn < x < 2 π + 2 πn

\frac{tan ( x ) - 5}{sec ( x )}

的值域:

- \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )} \leq f (x) \leq - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}

\frac{tan ( x ) - 5}{sec ( x )}

的轴截距点

:

X 截距

: (arctan (5) + 2 πn, 0), (arctan (5) + π + 2 πn, 0),

Y 截距

: (0, - 5)

\frac{tan ( x ) - 5}{sec ( x )}

的渐近线

:

无

\frac{tan ( x ) - 5}{sec ( x )}

的极值点:

极大值

(- arctan (\frac{1}{5}) + π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + π )}),

极小值

(- arctan (\frac{1}{5}) + 2 π + 2 πn, - \frac{26}{5 sec ( - arctan ( \frac{1}{5} ) + 2 π )})

作图

流行的例子

f(x)=(2x^2-3x-9)/(x-3)

y=sqrt(x/(9-x^2))