What is the tangent of 1/(sqrt(11x)) ?

The tangent of 1/(sqrt(11x)) is y=-1/(2sqrt(11)a_{0)^{3/2}}x+3/(2sqrt(11)\sqrt{a_{0)}}

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tangent of 1/(sqrt(11x))

tangent of

\frac{1}{11 x}

y = - \frac{1}{2 11 a _{0}^{\frac{3}{2}}} x + \frac{3}{2 11 a _{0}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{1}{11 a _{0}})

Find the slope of

y = \frac{1}{11 x} : \frac{d y}{d x} = - \frac{1}{2 11 x ^{\frac{3}{2}}}

Compute the slope of

y = \frac{1}{11 x}

x = a_{0} : m = - \frac{1}{2 11 a _{0}^{\frac{3}{2}}}

Find the line with slope m=

- \frac{1}{2 11 a _{0}^{\frac{3}{2}}}

and passing through

(a_{0}, \frac{1}{11 a _{0}}) : y = - \frac{1}{2 11 a _{0}^{\frac{3}{2}}} x + \frac{3}{2 11 a _{0}}

y = - \frac{1}{2 11 a _{0}^{\frac{3}{2}}} x + \frac{3}{2 11 a _{0}}

y = (1 + \frac{1}{x})^{2}

x \to 1 lim ([f (x) + 5 g (x)])

x + y \frac{d y}{d x} = x - y

f (x) = x^{3} - x, (1, 0)

n = 0 \sum \infty \frac{1}{n ( n + 8 )}

What is the tangent of 1/(sqrt(11x)) ?
The tangent of 1/(sqrt(11x)) is y=-1/(2sqrt(11)a_{0)^{3/2}}x+3/(2sqrt(11)\sqrt{a_{0)}}