What is the tangent of f(x)=(2x-1)/(x+5),\at x=1 ?

The tangent of f(x)=(2x-1)/(x+5),\at x=1 is y= 11/36 x-5/36

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tangent of f(x)=(2x-1)/(x+5),\at x=1

tangent of

f (x) = \frac{2 x - 1}{x + 5}, at x = 1

y = \frac{11}{36} x - \frac{5}{36}

Solution steps

Find the tangent point:

(1, \frac{1}{6})

Find the slope of

f (x) = \frac{2 x - 1}{x + 5} : \frac{df ( x )}{d x} = \frac{11}{( x + 5 ) ^{2}}

Compute the slope of

f (x) = \frac{2 x - 1}{x + 5}

x = 1 : m = \frac{11}{36}

Find the line with slope m=

\frac{11}{36}

and passing through

(1, \frac{1}{6}) : y = \frac{11}{36} x - \frac{5}{36}

y = \frac{11}{36} x - \frac{5}{36}

x \to - \infty lim (\frac{4 x ^{6}}{x ^{3} - 8})

θ \to \frac{π}{3} lim (\frac{tan ( θ )}{sin ^{2} ( θ )})

\int \frac{x ^{2}}{( x + 1 ) ^{50}} d x

\frac{\partial}{\partial x} (2 x e^{- y})

\int (2 x - 1) ln (17 x) d x

What is the tangent of f(x)=(2x-1)/(x+5),\at x=1 ?
The tangent of f(x)=(2x-1)/(x+5),\at x=1 is y= 11/36 x-5/36