What is the tangent of 2/(x-8) ?

The tangent of 2/(x-8) is y=-2/((a_{0)-8)^2}x+(4a_{0}-16)/((a_{0)-8)^2}

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tangent of 2/(x-8)

tangent of

\frac{2}{x - 8}

y = - \frac{2}{( a _{0} - 8 ) ^{2}} x + \frac{4 a _{0} - 16}{( a _{0} - 8 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} - 8})

Find the slope of

y = \frac{2}{x - 8} : \frac{d y}{d x} = - \frac{2}{( x - 8 ) ^{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{2}{( a _{0} - 8 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} - 8 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} - 8}) : y = - \frac{2}{( a _{0} - 8 ) ^{2}} x + \frac{4 a _{0} - 16}{( a _{0} - 8 ) ^{2}}

y = - \frac{2}{( a _{0} - 8 ) ^{2}} x + \frac{4 a _{0} - 16}{( a _{0} - 8 ) ^{2}}

\frac{d y}{d x} = \frac{5 x sec ( \frac{y}{x} ) + y}{x}

10 x - 6 y x^{2} + 1 y^{^{'}} = 0

x \to 0 lim (\frac{3 - cos ( x )}{x})

y^{^{''}} - 18 y^{^{'}} + 81 y = t^{2} e^{9 t} - e^{9 t}

y = 3 cos^{2} (x)

What is the tangent of 2/(x-8) ?
The tangent of 2/(x-8) is y=-2/((a_{0)-8)^2}x+(4a_{0}-16)/((a_{0)-8)^2}