What is the tangent of 1+sqrt(4-x) ?

The tangent of 1+sqrt(4-x) is y=-1/(2sqrt(-a_{0)+4)}x+1+sqrt(4-a_{0)}+(a_{0})/(2sqrt(-a_{0)+4)}

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tangent of 1+sqrt(4-x)

tangent of

1 + 4 - x

y = - \frac{1}{2 - a _{0} + 4} x + 1 + 4 - a_{0} + \frac{a _{0}}{2 - a _{0} + 4}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 1 + 4 - a_{0})

Find the slope of

y = 1 + 4 - x : \frac{d y}{d x} = - \frac{1}{2 - x + 4}

Compute the slope of

y = 1 + 4 - x

x = a_{0} : m = - \frac{1}{2 - a _{0} + 4}

Find the line with slope m=

- \frac{1}{2 - a _{0} + 4}

and passing through

(a_{0}, 1 + 4 - a_{0}) : y = - \frac{1}{2 - a _{0} + 4} x + 1 + 4 - a_{0} + \frac{a _{0}}{2 - a _{0} + 4}

y = - \frac{1}{2 - a _{0} + 4} x + 1 + 4 - a_{0} + \frac{a _{0}}{2 - a _{0} + 4}

\frac{1}{4 y}

2 y d x + x d y = 0

\int \frac{( x ^{2} + 1 )}{x + 1} d x

\int_{0}^{5} \frac{1}{25 + x ^{2}} d x

\int \frac{c}{x ^{2}} d x

What is the tangent of 1+sqrt(4-x) ?
The tangent of 1+sqrt(4-x) is y=-1/(2sqrt(-a_{0)+4)}x+1+sqrt(4-a_{0)}+(a_{0})/(2sqrt(-a_{0)+4)}