Engineering Calculus Notes 233

# Engineering Calculus Notes 233 - 221 3.1 CONTINUITY AND...

This preview shows page 1. Sign up to view the full content.

3.1. CONTINUITY AND LIMITS 221 2. For every ε> 0 there exists δ> 0 such that for points −→ x D 0 < dist( −→ x, −→ x 0 ) guarantees | f ( −→ x ) L | <ε. The ε - δ formulation can sometimes be awkward to apply, but for finding limits of functions of two variables at the origin in R 2 , we can sometimes use a related trick, based on polar coordinates. To see how it works, consider the example f ( x,y ) = x 3 x 2 + y 2 , ( x,y ) negationslash = (0 , 0) . If we express this in the polar coordinates of ( x,y ) x = r cos θ y = r sin θ we have f ( r cos θ,r sin θ ) = r 3 cos 3 θ r 2 cos 2 + r 2 sin 2 = r 3 cos 3 θ r 2 = r cos 3 θ. Now, the distance of ( x,y ) from the origin is
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern