What is the tangent of f(x)= 1/(x+8),\at x=5 ?

The tangent of f(x)= 1/(x+8),\at x=5 is y=-1/169 x+18/169

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tangent of f(x)= 1/(x+8),\at x=5

tangent of

f (x) = \frac{1}{x + 8}, at x = 5

y = - \frac{1}{169} x + \frac{18}{169}

Solution steps

Find the tangent point:

(5, \frac{1}{13})

Find the slope of

f (x) = \frac{1}{x + 8} : \frac{df ( x )}{d x} = - \frac{1}{( 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{1}{169}

Find the line with slope m=

- \frac{1}{169}

and passing through

(5, \frac{1}{13}) : y = - \frac{1}{169} x + \frac{18}{169}

y = - \frac{1}{169} x + \frac{18}{169}

x \to 4 - lim (\frac{( 1 - x )}{4 - x})

cos (6 x) (\frac{d y}{d x}) + 6 (tan (6 x)) y = 5 sec (6 x)

t \to 0 lim (cos (\frac{1}{t}))

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

\int \frac{e ^{- x} ( 3 + 4 x ln ( x ) )}{2 x} d x

What is the tangent of f(x)= 1/(x+8),\at x=5 ?
The tangent of f(x)= 1/(x+8),\at x=5 is y=-1/169 x+18/169