Bob

Hi, I have two limits to solve involving trigonometric functions, and I have been unable to get on the right path of manipulation to avoid an indeterminate form.

The first one is lim[x→0](x^2 cot^2(3x)). I tried using a Pythagorean identity, but then csc(0) is undefined. A hint that my teacher gave is the well-known limit: lim[x-->0](sin(x)/x)=1, but I have been unable to get the beginning expression to resemble this at all.

The second one is lim[θ→0]((2sinθ-sin2θ)/θ^3)). His tip was to start with the double angle formula, which is sin2θ=2sinθcosθ. But I got stuck after trying that. He also says to remember the same limit that I stated above involving sin(x)/x.

Any help would be much appreciated, as these problems have had me stumped for a little while. Thanks.

I am currently a sophomore in high school, and I take AP Biology and AP European History. I have an A+ in both classes. I took AP Environmental Science as a freshman, and I got an A and a 5 on the exam. I also currently take Trig/Pre-calculus Honors, English 10 Honors, Chemistry Honors, and Spanish III. Next year, I plan on taking AP Calculus BC, AP Physics C, AP US History, AP English Language, AP Chemistry, Spanish IV Honors, and something else. The main two classes I'm not sure about are Calc BC and Physics C. I could instead take Calc AB and Physics 1, but I would prefer to take the harder two. I am very good at math, and I have a 100 in Math Analysis/Trig Honors. I have heard from a sophomore who takes BC that as long as you have a good trig foundation and are able to learn quickly, BC is doable. I also want to major in Physics, so I would like to take Physics C next year and Physics 2 senior year. Is Physics C too difficult to take without any background in physics or calculus? I am an all-A student, but I am just wondering whether or not these courses are too difficult. Thank you.

I was learning to drive a manual transmission in my mom's car. I was doing okay at first, but then when trying to accelerate from a stop, I accidentally went into third gear instead of first, causing the car to kind of jerk and lurch forward and make sort of a grinding noise. I did this a few times, and smoke started coming out of the exhaust with a pretty bad smell. The car seemed to drive fine afterwards, but I'm still worried about it. Does it sound like any major damage was done? Thanks in advance for your help.

Yesterday, I was practicing rolling forward on the ground for Taekwondo. When I was coming up, my left foot hit a chair, and my face smashed into my knee. My nose started bleeding instantly out of the left nostril, and it was throbbing for about an hour or two after. I always have nose bleeds out of my left nostril, probably due to dryness, and I had actually had one just a day or two before the impact. Earlier today, I was trying to clean out my nose with a tissue and it started bleeding again out of the left nostril. My nose doesn't look crooked, swollen, or discolored, but I feel pressure on it most of the time. If I touch the lower bridge of my nose or the upper cartilage, I feel a bruise-like pain. Should I go to the doctor? Thanks for any help.

I am a 14 year old male, and I have had swollen lymph nodes in the neck for at least two years. I noticed the first one about two years ago on the back left of my neck near the middle. It is about two cm and hasn't changed as far as I know. It is hard but mobile. I also noticed some on the mastoid behind the ear a little after that which are about one to 1.5 cm at the most. These aren't as hard, but they are not mobile. A little later, I noticed one behind both sides of my jaw, below the ear. I think this is part of the salivary gland. I also noticed a fairly large, 1.5 cm lump in my right submandibular gland. This one is quite hard but very mobile and it hurts if I squeeze it sometimes. Sometimes these nodes will cause me pain in the back of the neck, especially a dull ache at the mastoid. I also have had IBS symptoms for at least two years, with lots of bloating and some abdominal pain. I will occasionally get random chest pains. I recently started having shortness of breath, which I attributed to anxiety, because I only noticed it when I was thinking about it. In the past week or two, I started having lots of symptoms in the salivary glands. I will sometimes get random aches when I yawn or chew. They also seem to be swollen. I get dry mouth when I wake up, but it usually goes away by the end of the day. I noticed a few somewhat hard, small lumps below my chin and above the trachea (bottom of jaw). I have had very mild post nasal drip for a long time now. It feels like I always have to swallow mucus. I have also been having occasional dry eyes, so I was thinking I might have Sjogren's syndrome, since it can mimic lymphoma. I know I should see a doctor, but I was hoping I could get some opinions. Thank you.

I am a 14 year old male, and I have been having shortness of breath on and off for the past month or so. I will also occasionally get other symptoms like a feeling of something in the throat and heart palpitations. I only notice the shortness of breath when I am not busy. If I am at school with friends or doing physical activity, I don't notice it. This makes me think that it isn't a physical cause. However, I've also had swollen lymph nodes in the neck for the past two years or more and swollen lymph nodes in the salivary glands for maybe a year. I have been having IBS like symptoms (bloating, constipation, gas, etc.) for the past few years as well. I've always been a pretty anxious person for as long as I can remember, so I think I might have an anxiety disorder, and I was just looking for some opinions and/or tips. Thanks.

I am a 14 year old male, and I started having shortness of breath about a week and a half ago. It started around 2:00 or 3:00 PM at school, a few hours after we did an Insanity workout in gym class (I don't know if that may have caused hyperventilation or something). I wasn't really noticing it until later when I went to my dad's house. We were watching an action movie, and I started focusing on my breath a lot and had a small panic attack. I was having really bad shortness of breath that whole weekend. During the school week, the symptoms were less noticeable. We've had a four day weekend so far due to weather, and I stopped really having shortness of breath yesterday (Monday). However, I started having a feeling of a lump in the throat and mucus in the back of my throat. I've also had burping and a little bit of heartburn mainly when bending over. It started getting really bad when I thought about it, but when I am occupied, I don't notice it. I have also been having symptoms similar to IBS for the past few years, but I haven't talked to a doctor about that. These symptoms have been making it difficult for me to fall asleep, and I wake up multiple times during the night. I usually wake up with bad dry mouth which gets better as the day goes on. I'm pretty sure these are caused by anxiety, because I have been having some family problems lately. I think that these symptoms may be causing me to be more anxious, which is in turn exacerbating the symptoms. I am thinking of visiting a doctor soon, but I wanted to know if you guys think this is just anxiety.

I am a 14 year old male, and I have had symptoms of lymphoma for at least two or three years. It started when I found a swollen lymph node on the back left side of my neck about two and a half years ago. It is about 2 or 3 cm and has not grown in a long time. I later started having IBS-like symptoms, which I still have occasionally. I found swollen lymph nodes in my groin a while ago, and I recently found my salivary glands to be swollen, with lumps below the ears and one on the right side below my jaw. Most of these lumps are hard and immobile. I have had dehydration issues in the past causing dizziness. I recently started having shortness of breath, which I have had before. But it has lasted for about four or five days this time. I have been hyperventilating somewhat. I have also had anxiety and depression in this past time. I'm not sure if this is being caused by the shortness of breath or vice versa. I have also had some family issues lately, and my mom is depressed, so this could maybe have led to anxiety/depression. I've also been having bloating after eating and belching. I have also been having fatigue recently. I know I have a lot of symptoms, but I would think that it would be more serious by now. I read that low grade lymphoma is unheard of in people my age. I know I should visit a doctor, which I plan on doing soon, so please don't just tell me to go to the doctor. Thanks.

I am about 14.4 years old (I was born on April 7th, 1999), and I am almost exactly 5'9" in height. I started school recently, and I seem slightly above average height for guys in my grade. But, I am one of the youngest people in my grade. Most kids are 15. My mom is 5'4" or 5'5" I think, and my dad is about 6'2". What is a good estimate of how tall I might be when I am fully grown? If it matters, I grow facial hair mostly as a mustache and on my chin, so I usually shave about once or twice a week. Also, I weigh about 130 lbs. Is this too skinny for my age and height? Thanks.

I am fourteen years old, and my brother is almost nineteen. He, my sister, and I live with my mother, who works full time. My dad lives very close by though, so we stay with him every other weekend and see him a lot. My brother has had a drug problem for a while. Over the past few years, my family and I have noticed many things go missing. I had a PS2 and a Nintendo DS Lite complete in box and they magically disappeared, along with the cables. He denied having anything to do with it. One time I actually caught him taking sixty dollars out of my wallet, which is in a good hiding spot. He just laughed it off. I notice that things in my room have been slightly rearranged sometimes, so he is searching for money. I have many very rare games and things that I would be very upset if I lost. He has been staying at my dad's house for the last week or so, and multiple things have disappeared from my dad's house. First of all, sixty dollars went missing from my dad's wallet, and my brother and his girlfriend were the only other people in the house. Also, a bag of very valuable silver coins which belonged to my deceased grandfather went missing, and something that was in the bag was on the closet floor. My dad also noticed a ring missing. My brother asks my mom for twenty dollars literally every day, and he gets very mad if she says no. If he is ever confronted about the stealing, he gets very angry, firmly denies it, and either leaves or hangs up the phone. He is also very annoying and always makes fun of me or tries to touch me inappropriately as a joke. I have also noticed that he downloaded tons of porn on my laptop. I have put a password lock on my computer since then. He did the same on my dad's computer, and he has gotten a virus on the computer multiple times which won't allow you to access any programs and says the FBI is monitoring your computer. He has a job, but he barely ever goes. He is going off to college next month, but I highly doubt that will last long. He sets an alarm for school, but it rings hundreds of times before my mom has to wake him up. My dad is thinking of kicking him out of his house, but I know my mom won't do that. I wouldn't call the police on him myself, but any advice would be helpful.

I'm looking for more metal bands to listen to. I mainly like heavy metal, thrash metal, and death metal. I also like a little bit of some other genres. The only subgenre I hate is nu metal, so don't recommend any of that. My favorite classic metal bands are Black Sabbath, Ozzy Osbourne, Iron Maiden, Judas Priest, Halford, Dio, and Rainbow. My favorite thrash metal bands include Slayer (my favorite band), Megadeth (close second), early Metallica, Anthrax, Sodom, Kreator, Overkill, Exodus, and Testament. My favorite death metal bands are Cannibal Corpse, Death, Deicide, Morbid Angel, Suffocation, and Six Feet Under. I would like some bands that are similar to those that I listed. It would also be helpful if you listed the best albums of those bands.

Christians (not all, but many) always say that homosexuality is a sin because of Leviticus 18:22. First of all, that passage is in the Old Testament, so why do you even follow it? Secondly, the Old Testament mentions so many other ancient and archaic laws and guidelines that nobody follows today. An example is that somewhere in the Torah, it says that if a man finds his wife not to be a virgin, she should be stoned. If homosexuals shouldn't be allowed to marry, why should non-virgins? Another idiotic passage states that you may not round off you haircut, whatever that means. It also forbids tattoos, and I have seen pictures of moron rednecks who tattoo Leviticus 18:22 on their arms. I am just wondering if any of you can come up with more than a half-assed excuse as to why you constantly preach hate against homosexuality.

A company makes two cylinders. The smaller cylinder has a surface area of 0.81 times the surface area of the larger cylinder. The larger cylinder has a height of 60.

The formula for surface area of a cylinder is 2*pi*r(h+r). I can't figure out how to do this problem at all. Any help would be appreciated.

I am currently in eighth grade, and I am enrolled in Geometry, Earth Science, Advanced English, World History & Geography I, and Health & PE 8. My two electives are Spanish I and Technology Foundations. I have gotten all As in those classes so far, so I am one of the best students at my school. Next year, I will be enrolled in Honors Algebra II, Honors English 9, Honors World History & Geography II, Honors Biology, and Health & PE 9. My first elective will be Spanish II. For my second elective, I plan on taking AP Environmental Science. Few Freshmans take this class, because you must be reccomended for Honors Biology and get a teacher reccomendation for AP Environmental. Will this be too hard for me? I think I can do it, but I will probably have tons of work every day. The main benefit of taking this AP class is that I won't have to do an independent project for Biology. This is also a class that I would probably enjoy. I would highly appreciate anyone who has experience to help me out. Thanks!

I just beat Erika in Pokemon Blue, and I don't know which Pokemon I should use to round out my team. My team right now is:

1. Wartortle lvl. 30: Bite, Bubblebeam, Ice Beam, Water Gun

2. Pikachu lvl. 29: Thunderbolt, Thunder Wave, Flash, Mega Punch

3. Dugtrio lvl. 30: Dig, Rock Slide, Scratch, Sand-Attack

4. Alakazam lvl. 30: Psybeam, Confusion, Teleport, Kinesis

5. Flareon lvl. 31: Ember, Body Slam, Quick Attack, Sand-Attack

6. Pidgeotto lvl. 23 (used only for FLY)

Of course, I want to replace Pidgeotto, because Pidgeot isn't very useful later in the game. Some of the Pokemon I was thinking of were Snorlax, Machamp, Exeggutor, or Dragonite. I think a physical attacker or some sort of wall would be best. I would appreciate suggestions on which Pokemon I should use for the final slot and a moveset. I would also appreciate any move suggestions for my other Pokemon, but please keep in mind that they are still low levels, so their movesets are subject to change over time anyway. Also keep in mind that I have limited access to TMs, and I don't want to use the Missingno. glitch. I have used it in other games, and it screws up the Hall of Fame.

I am 13 years old. I was baptized and raised Catholic. I received first Communion and I had my first confession years ago. After my parents split up, we stopped going to church regularly. Now, we only go on holidays or on some random days. During that time, I became an atheist for a short period. Now I believe in God again, and I am a Catholic again. I am very interested in my religion, but we still don't go to church often. I was just wondering if I have to do anything to become a Catholic again. Do I have to confess or something? Please no stupid answers saying that God isn't real or that I am a sinner or something. Thanks for your help!

I am 13 years old, and I was raised as a Catholic. I have always doubted God, though. When I was fairly young, we would go to church every Sunday. We stopped going, and my parents got divorced a few years later. I live with my mother, who isn't very religious. When my parents were married, she was supposedly a Catholic, but now she never talks about it. She only ever goes to church when my religious grandmother comes to town. My father is a non-practicing Catholic. I know he believes in God, because he went to Catholic school and he says that we should go to church more. He usually makes me go to church on religious holidays, but that's about it. I guess I don't really mind going to church, but it is boring and stupid. I have told a few of my friends that I am an atheist, but my parents don't know. Do you think I should tell them? I don't know if there is really even a point of telling them. Please no answers from religious people saying that I will go to hell. Thank you for any help.

I am confused about the notation for a plane in Geometry. I understand the notation where you just write three coplaner points. My teacher tells us to use a capital cursive letter for the other notation. I have also heard to just use a capital print letter. I would like to know the correct notation. Any help is greatly appreciated!

I just bought one of those new Magnavox Odyssey game systems. I took it out of the box and then I went to plug it into my new black and white 20 inch TV. I started playing that new game "Game No. 3," which I heard had great reviews. I tried to play it, but it was way too complicated for me to understand! There are two dots, one on each side. There is also a dot that moves around the screen. It took me like 20 minutes to find out that you use the left controller for the left dot and the right controller for the right dot. Are you supposed to have two people or something?! I'm used to that old game "Call of Duty," where you only use like 15 buttons. And then, I tried that game that people rave about, "Game No. 1." This, time there is only one dot. This game is so complicated, that I can't even figure out what to do! What do I do with this insane dot?!?! It's so hard! Can somebody please tell me how to use this infernal contraption?!?!?!?!