The improper integral f(x) dx cannot be converted into an integral with finite limits using the substitution t = \/x because the limit at zero becomes infinite. The problem is resolved by first writing/0 fix) dx = J() f(x)dx4-J] fix) dx. Apply this technique to approximate the following improper integrals to within I0-6 . roo \ \ a. / 7 dx b. / r ~ dx Jo ' + x Jo (1+x2 )

MATH 2010 – Multivariable Calculus & Matrix Algebra Professor Herron – Rensselaer Polytechnic Institute Week 2 (2/1/16 – 2/5/16) Important: These notes are in no way intended to replace attendance in lecture. For best results in this course, it is imperative that you attend lecture and take your own detailed notes. Please keep in mind that these notes are written specifically with Professor Herron’s sections in mind, and no one else’s. There were no important pictures or diagrams in lecture this week, so I will not be placing images in this set of notes. Gradients - Two kinds of functions Real value functions o = , = ( ⃑ Vector value fu