Question

find the radius of curvature of the curve y=x³at(1,1)​

Answer 1

Answer:

Sorry dear my maths is too weak I am really sorry

Answer 2

The radius of curvature of the curve y=x³at(1,1)​ is $\frac{5\sqrt{10} }{3}$.

Step-by-step explanation:

Given:

The curve $y=x^{3}$.

To Find:

The radius of curvature of the curve y=x³at(1,1)​.

Solution:

As given-the curve $y=x^{3}$.

$y=x^{3}$

$\frac{dy}{dx} =3x^{2}$

$\frac{dy}{dx}|_{(1,1)} =3\times 1^{2}=3$  

     

$\frac{d^{2} y}{dx^{2} } =6x$

$\frac{d^{2} y}{dx^{2} }|_{(1,1)} =6\times 1 =6$

$Radius\ of\ Curvature\ Z=\frac{(1+(\frac{dy}{dx} )^{2} )^{\frac{3}{2} } }{|\frac{d^{2}x }{dy^{2} } |}$

                                        $=\frac{(1+(3 )^{2} )^{\frac{3}{2} } }{|6 |}$

                                        $=\frac{(1+9 )^{\frac{3}{2} } }{|6 |}$

                                        $=\frac{(10 )^{\frac{3}{2} } }{|6 |}$

                                        $=\frac{(1000 )^{\frac{1}{2} } }{|6 |}$

                                       $=\frac{10\sqrt{10} }{6}$

                                       $=\frac{5\sqrt{10} }{3}$

Thus, the radius of curvature of the curve y=x³at(1,1)​ is $\frac{5\sqrt{10} }{3}$.

                                         

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