What is the tangent of 1/(x-7) ?

The tangent of 1/(x-7) is y=-1/((a_{0)-7)^2}x+(2a_{0}-7)/((a_{0)-7)^2}

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tangent of 1/(x-7)

tangent of

\frac{1}{x - 7}

y = - \frac{1}{( a _{0} - 7 ) ^{2}} x + \frac{2 a _{0} - 7}{( a _{0} - 7 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{a _{0} - 7})

Find the slope of

y = \frac{1}{x - 7} : \frac{d y}{d x} = - \frac{1}{( x - 7 ) ^{2}}

Compute the slope of

y = \frac{1}{x - 7}

x = a_{0} : m = - \frac{1}{( a _{0} - 7 ) ^{2}}

Find the line with slope m=

- \frac{1}{( a _{0} - 7 ) ^{2}}

and passing through

(a_{0}, \frac{1}{a _{0} - 7}) : y = - \frac{1}{( a _{0} - 7 ) ^{2}} x + \frac{2 a _{0} - 7}{( a _{0} - 7 ) ^{2}}

y = - \frac{1}{( a _{0} - 7 ) ^{2}} x + \frac{2 a _{0} - 7}{( a _{0} - 7 ) ^{2}}

\int \frac{7}{3 x} d x

\frac{\partial}{\partial t} (2 s^{2} + t^{2})

x \to 0 lim (1 + \frac{1}{x})

\int x e^{x^{3}} d x

What is the tangent of 1/(x-7) ?
The tangent of 1/(x-7) is y=-1/((a_{0)-7)^2}x+(2a_{0}-7)/((a_{0)-7)^2}