What is the tangent of x+3/x ?

The tangent of x+3/x is y=(1-3/(a_{0)^2})x+6/(a_{0)}

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tangent of x+3/x

tangent of

x + \frac{3}{x}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

y = x + \frac{3}{x} : \frac{d y}{d x} = 1 - \frac{3}{x ^{2}}

Compute the slope of

y = x + \frac{3}{x}

x = a_{0} : m = 1 - \frac{3}{a _{0}^{2}}

Find the line with slope m=

1 - \frac{3}{a _{0}^{2}}

and passing through

(a_{0}, a_{0} + \frac{3}{a _{0}}) : y = (1 - \frac{3}{a _{0}^{2}}) x + \frac{6}{a _{0}}

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

\int 24 tan^{3} (x) d x

y = 3 x, x = 1

y^{^{'}} - 3 y = e^{2 x}

\int (x - 6) d x

x \to 0 lim (\frac{e ^{x} - ( 1 - x )}{x})

What is the tangent of x+3/x ?
The tangent of x+3/x is y=(1-3/(a_{0)^2})x+6/(a_{0)}