Cowculus 3 



This box is the third in a series of letterboxes with Calculus clues. Thanks to Zfan for the idea...apologies to Leapin' Lizards and other mathphobics :)  
Students and parents of students should read my introduction to letterboxing before seeking the boxes. 

Solve the following Calculus problems, then enter the answers into the following narrative to find the box.  
1) The position of a particle is given by s(t) below. At what time will its acceleration be 30? A = _______


2) Find the maximum of the function f(x) = 3x^{2} + 42x + 133. B = ______  
3) A particle moves along the x axis with the following velocities:
Find the total displacement of the particle over t = (0,5) using the trapezoidal rule. C = _______ 

4) Solve the initial value problem below to find the value of the constant
term. D = _____


5) Find the total distance (not displacement) that a particle travels over t = 0 to t = 8, that has the following velocity. E = ______


6) Oh no! You thought you had just finished Navy Seal training, but you
were wrong. It turns out your captain has a surprise for you. Part
of your training is to be able to think on the spot and in every situation.
Before you can officially be inducted as a Navy Seal, you have to compute one
last test. The consequence if you don't complete the test is life or
death! You have to solve this math problem in 10 seconds...
GO!
10, 9, ..., Hurry up! The clock is ticking...6, 5, ... Time is almost up!.. 3, 2, ... 

7) First find the sum of the following convergent series: Next, find the first 3 nonzero terms of the Maclaurin expansion for f(x) = xsin2x. Enter the value for the sum of the series above in for x, and round the value to the nearest whole number. G = ______ 

8) Find the area enclosed by the polar graph


Did you know that there is a secret training ground for future Seal Team members
located in the humble town of West Bend, WI? Go and check out the facility
if you feel you have the stamina...and the smarts... Park your car on the corner of 6th and Decorah. Head over to the vacantlooking lot on the NE corner and find the rock with a tribute to a old veteran. Find the date on which he enlisted and multiply the month times the day. Remember this number for later. Remember  you are a Seal in training, so no writing down important information in case you are captured! Practice your memorization skills! Now for your endurance test. Carefully cross over to the south side of Decorah and take the sidewalk west up the hill. Real Seals run up the hill with a heavy pack in combat boots. We dare you to... Stop running when you see the asphalt path entrance to the training facility. Those without proper clearance only know of this place as a city park, but you are cleared to know it as the training grounds it truly is. As you enter the facility, you will notice the warning that this is NOT a place for those who get dogtired easily. Note also the climbing fence to the right. Continue on the path heading south. You will pass the beach training ground, then check out the basic obstacle course. Here future Seals practice their animal identification, climbing, and airplane evacuation skills. There is also a place to practice withstanding Gforces and dizziness, and to train on only the most modern of military vehicles. Continuing on the path south between training grounds, off to the right in the distance you will see the area where future Seals train for tunnel combat. Soon you'll pass the advanced training area. Here future Seals develop their rope swinging and zipline skills. If a recruit makes it through the rigorous training described so far, they can try out the expert training area a bit further south. Here you can see they practice evacuating larger planes, fight against extremely large beasts, scale castle walls, and do rock climbing. Have you survived all this training? There are a few more "hoops" you have to go through. As you transverse this area, be careful not to be hit by flying artillery from the practice range to the west. They say the grass is always greener on the other side, but after you've been through all the hoops, you'll see there is a "memorial" to a "fallen one" in the ground nearby. Go over and stand on top of the memorial to pay tribute. Did you do your class work? To become a Seal, one must not only endure rigorous physical training, but one must also endure the highest mental training as well! If you did your Calculus right, you can now proceed on the final test. Walk on a bearing of A = _____ for F = ______ steps. This will get you to one of the entrances of the sylvan training grounds. Enter the training ground and run up the hill, taking the path bearing G = _____ degrees at the split. At the next intersection, stop and practice your camouflage skills to hide from the attack squirrels.* These are actually small robots made to look and act like squirrels. They have been programmed with both combat and spy capabilities. Unfortunately, they were only issued one pair of squirrel underpants (cf. HalfEmpty HH) for the lot of them, and they mostly spend their time fighting each other over the one pair. Be careful not to get caught up in their inside fighting! Escape the squirrel area by taking the trail at a bearing of D = ______. At the next intersection, head on a bearing of H = _______. At the next intersection, do NOT head at B = ______ degrees, but take the other path. Next head at E = _______ degrees. Terrorists must be nearby. Notice the tall guy with his head lopped off on the left. Seals must train to be disciplined when faced with such dangers! At the next intersection you will need to travel on the path at C = _______ degrees. Do you remember the number from the tribute rock at the start? Walk that many steps down the trail. If you have successfully completed your Seal training, you can get your Seal seal in the sealed box sealed in the ground next to the stump in the woods to your right. Congratualtions! 

Before you set out read the waiver of responsibility and disclaimer. 