What is the tangent of x^2-2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

tangent of x^2-2

tangent of

x^{2} - 2

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

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

Compute the slope of

y = x^{2} - 2

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

Find the line with slope m=

2 a_{0}

and passing through

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

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

\frac{d}{d x} (- \frac{1}{( x - 3 ) ^{2}})

6 x - x^{2}

\int \frac{1}{x ^{2} + 81} d x

y = \frac{10}{ln ( x )}

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