What is the tangent of ((x^2))/(x+2) ?

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

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tangent of ((x^2))/(x+2)

tangent of

\frac{( x ^{2} )}{x + 2}

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{a _{0}^{2}}{a _{0} + 2})

Find the slope of

y = \frac{x ^{2}}{x + 2} : \frac{d y}{d x} = \frac{x ^{2} + 4 x}{( x + 2 ) ^{2}}

Compute the slope of

y = \frac{x ^{2}}{x + 2}

x = a_{0} : m = \frac{a _{0}^{2} + 4 a _{0}}{( a _{0} + 2 ) ^{2}}

Find the line with slope m=

\frac{a _{0}^{2} + 4 a _{0}}{( a _{0} + 2 ) ^{2}}

and passing through

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

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

x \to 0 lim (\frac{cos ( \frac{π}{2} - x )}{x})

n = 2 \sum \infty 5 \cdot (- \frac{3}{4})^{n}

y^{^{''}} + 5 y^{^{'}} + 4 y = t^{2} e^{7 t}

\int_{0}^{l n (5)} e^{x} - e^{- 2 x} d x

\int_{0}^{6} \frac{6 t}{( t - 7 ) ^{2}} d t

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