Please type your full name in each of the spaces below to sign the FIU Academic Integrity Pledge. These signatures are required to receive credit for this exam. As a student of this university: I, [name] am honest in my academic endeavors and do not represent other’s work as my own I, [name] do not cheat, nor do I aid others in cheating I, [name] understand that if am found responsible for academic misconduct, I will be subject to Academic Misconduct procedures and sanctions as per the Student Conduct and Honor Code.

Extra Credit: You have about 50 potato plants, which are distributed between two greenhouses.  This year, you notice that the potato plants are growing poorly. Upon closer inspection, you notice aphids, which are small insects, crawling all over your plants. While there are several different ways to deal with an aphid infestation, you decide to “experiment” with a biocontrol approach. Biocontrol, or biological control, is an approach to controlling pests using other organisms.  Ladybugs are a known predator of aphids. You go to your favorite nursery and purchase some ladybugs. The next evening you release the ladybugs in both greenhouses.  Some fly away, but the majority take up residence on your plants.  One week later you notice that your plants seem to be much healthier, and there are far fewer aphids on them. Given your experimental set up, is it safe to conclude that ladybugs did the trick and solved your aphid problem? Explain.

Write a Maclaurin series for 63+x{“version”:”1.1″,”math”:”63+x”}.

Determine the convergence or divergence of the series.  Name any series test(s) used. ∑n=1∞n35n2+3{“version”:”1.1″,”math”:”∑n=1∞n35n2+3″}

Select all of the terrestrial planets in our solar system. 

If parametric equations for a curve are  x=2t and y=t+2, {“version”:”1.1″,”math”:”x=2t and y=t+2, ”} with 0≤t≤5{“version”:”1.1″,”math”:”0≤t≤5″}, what does 2π∫055(t+2)dt{“version”:”1.1″,”math”:”2π∫055(t+2)dt”} represent?

Determine the convergence or divergence of the series ∑n=0∞5-1nn!3n{“version”:”1.1″,”math”:”∑n=0∞5-1nn!3n”}

Evaluate the integral by hand:  ∫sec3ϖtan3ϖdϖ{“version”:”1.1″,”math”:”∫sec3ϖtan3ϖdϖ”}.

Integrate ∫4y2e2ydy{“version”:”1.1″,”math”:”∫4y2e2ydy”}

Set up integral(s) representing the volume of the solid generated by revolving the region bounded by x=0,y=0,y=6{“version”:”1.1″,”math”:”x=0,y=0,y=6″} and y=x-4{“version”:”1.1″,”math”:”y=x-4″} about the line x=10{“version”:”1.1″,”math”:”x=10″}.  a.  Use shells. b.  Use disks/washers. c.  Evaluate one of the integrals.  Record the exact answer, not an approximation.