What is the tangent of 2/(x-5) ?

The tangent of 2/(x-5) is y=-2/((a_{0)-5)^2}x+(4a_{0}-10)/((a_{0)-5)^2}

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tangent of 2/(x-5)

tangent of

\frac{2}{x - 5}

y = - \frac{2}{( a _{0} - 5 ) ^{2}} x + \frac{4 a _{0} - 10}{( a _{0} - 5 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 5})

Find the slope of

y = \frac{2}{x - 5} : \frac{d y}{d x} = - \frac{2}{( x - 5 ) ^{2}}

Compute the slope of

y = \frac{2}{x - 5}

x = a_{0} : m = - \frac{2}{( a _{0} - 5 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} - 5 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} - 5}) : y = - \frac{2}{( a _{0} - 5 ) ^{2}} x + \frac{4 a _{0} - 10}{( a _{0} - 5 ) ^{2}}

y = - \frac{2}{( a _{0} - 5 ) ^{2}} x + \frac{4 a _{0} - 10}{( a _{0} - 5 ) ^{2}}

\int \frac{- 1400 x}{25 - x ^{2}} d x

\frac{d}{d x} (sin (x) cos (x) + sin (x))

x^{3} + x^{2}

x \to \infty lim (\frac{m}{n})

n = 0 \sum \infty 0.0 1^{n}

What is the tangent of 2/(x-5) ?
The tangent of 2/(x-5) is y=-2/((a_{0)-5)^2}x+(4a_{0}-10)/((a_{0)-5)^2}