Thursday

October 23, 2014

October 23, 2014

Posted by **Nadine** on Monday, December 14, 2009 at 9:03am.

- Calculus -
**MathMate**, Monday, December 14, 2009 at 10:00amUsing implicit differentiation, find the slope of the tangents

y'=x/y

The slopes of the normals are therefore:

y'=-y/x

Rearrange and integrate

∫y'/y = ∫-1/x

ln y = -ln x + C1

ln y = -k ln x

raise to the power of e:

y=C/x

This is the family of reciprocal curves, or rectangular hyperbolas.

**Answer this Question**

**Related Questions**

Math - Mark each of the following True or False. ___ a. All vectors in an ...

Math - The functional determinant of x, e^x, and e^-x is equal to___ The ...

calculus - two curves are orthogonal at a point of intersection of their ...

Calculus - Orthogonal Trajectories - Find the orthogonal trajectories of the ...

Math - Vectors - Prove that vector i,j and k are mutually orthogonal using the ...

Linear Algebra, orthogonal - The vector v lies in the subspace of R^3 and is ...

calculus - if the tangent of two intersecting circles, at their points of ...

Calculus - Resolve u=[3,4,7] into two orthogonal vectors, one of which is ...

Calculus - Resolve u=[3,4,7] into two orthogonal vectors, one of which is ...

Math - I'm doing a bunch of practice finals and I don't know how to approach ...