AboutScotto Expertise Any kind of mathematics (algebra, geometry, trigonometry, matrices, calculus, linear approximation, linear regression, linear programming, numerical analysis, probability, statistics, etc.). I also have answered some questions in Physics, Chemistry, and Biology. I would like to volunteer in all areas of Mathematics, not just calculus, and the other three courses that were mentioned.
Experience Experience in the area: I have tutored students in all areas of mathematics for over 20 years.
Education/Credentials: BSand MS in Mathematics from Oregon State University, where I completed sophomore course in Physics and Chemistry. I received both degrees with high honors.
Awards and Honors: I have passed Actuarial tests 100, 110, and 135.
Question I need to do a delta-epsilon proof for the limit as {x goes to (5pi)/3} for cosx. I
kind of understand how to do a delta-epsilon proof but not very well versed in
it. i looked at this problem and had no idea. Thanks alot.
Answer Using the Taylor's polynomial to approximate the cos(x) curve around x=2π/3, we get f(x)≈-1/2 + (√3/2)δ.
We know that δ/2<(√3/2)δ≈ε at x=2π/3. What this tells us is that we need δ<2ε as long as δ<1/2 (remember that delta is suppose to be small, almost 0, so it's definitely less than 1/2).
