What is the tangent of x^2-1 ?

The tangent of x^2-1 is y=2a_{0}x-a_{0}^2-1

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tangent of x^2-1

tangent of

x^{2} - 1

y = 2 a_{0} x - a_{0}^{2} - 1

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0}^{2} - 1)

Find the slope of

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

Compute the slope of

y = x^{2} - 1

x = a_{0} : m = 2 a_{0}

Find the line with slope m=

2 a_{0}

and passing through

(a_{0}, a_{0}^{2} - 1) : y = 2 a_{0} x - a_{0}^{2} - 1

y = 2 a_{0} x - a_{0}^{2} - 1

\int_{1}^{4} 8 x ln (x) d x

\int (x^{3} + 4 x y) d x

\int_{0}^{1} (x^{2} + 1) (e^{- x}) d x

\frac{1}{s ^{2} + 4 s + 8}

g (x) = \frac{3}{6 x + 8}