Calculus help please In one of the final assignments for my calculus class, I got this one question I don't know what to do with this one. Here's the question: If a0, a1, a2...,and an are real numbers that satisfy (a0/1) + (a1/2)...+(an/(n+1)) = 0 show that the equation a0 + a1x + a2x^2...+ anx^n = 0 has at least one real root. --------------------------------- NOTE: a0, a1, a2, an= a subscript 0, a subscript 1, a subscript 2, a subscript n x^2, x^n = x to the 2nd power, x to the nth power. I must use mean value theorem for integral
proud of my dog Yesterday, just before noon, I was on my laptop checking out school-related stuff. I heard my dog randomly bark (my dog never barks unless there's an animal or lawnmowers). Then he walked out of my room and suddenly, he barked incessantly but his bark was different. I felt like my dog was really mad. I yelled at my dog from my room "HEY!". My dog would usually stop but he didn't. I looked out my window only to find out that some guy in black leather jacket and dark cargo pants trying to sway off my dog who was all over him. I quickly ran to the kitchen, grabbed a 2 steak knives and when I got a chance to get to my backyard, I saw the jump dowwn the fence of my yard and my dog standing on the gate. Few seconds later
Calculus proof help please I really need help on this one proof and I've already attempted it but I'm no sure if it makes any sense! Here are a couple of this to remember to understand what I'll type... abs() = absolute value of something x->a = x approaches a e = epsilon d = delta ----------------------------- Here's the problem If lim f(x) = L as x->a, where L<0, then there exist N(a, e) such that f(x)<0 for every x in N(a,e) Prove that the statement above is true ----------------------------- My Attempt Nothing...I'm stumped...I don't even know how to start this other than... Let e > 0 and d > 0 That means abs(f(x) - L) < e and abs(x-a) < e I guess...substitute L with (-L) so, that will make it abs(f(x) + L) <
Physics help please I feel a little lost. Here's the scenario. There are two objects m and M are connected by a string that goes through a pulley on an incline. The incline is 45 degrees from the horizontal. m = 4Kg and M = 10Kg and theta (@) = 45 degrees. I am assuming that m is only the inclined plane and M is hanging on the string. Do not consider friction. a) what forces are acting on each object? I got the horizontal and vertical components of the gravitational force on m. I got Fy = mgsin@ and Fx = mgcos@. For m, I have F in the y = Normal force - mg(sin@). F in the x = Tension - ma(cos@) For M, I have F = T - Mg. b) calculate the accel. for the objects For M, I wrote that the accel for M is gravity (-9.8m/ss). If the system is still
Fate/Zero Questions spoiler I just finished watching the last episode. Holy crap! this anime is amazing! I usually hate guns and stuff but freakin' Kiritsugu was badass! I felt bad for Kariya since the beginning; I wanted him to win even though I knew Kiritsugu was going to win. Anyway, I'm a little puzzled with a few things. Do note, I have only watched the anime of Fate Zero and Fate Stay Night. - How the heck was Aoi Tohsaka (Rin's mother) revived at the end? Was her memory/mental issue a by product of her vivification? - Was Sakura Tohsaka really just a lil' B? Has she seriously lost her heart? - Speaking of Sakura, wasn't she supposed to be the next mage for the Mutou family but why is she not the family's mage in Fate Stay Night? How
My guilt is seriously bugging me I need to vent this out. I returned home from an exhausting school day. I went straight to my back yard and hung out with my awesome dog. He's running around, sniffing all over, and barking at anything that steps into our yard. Anyway, my bad eyes suddenly became accurate and spotted a HUGE grasshopper...it was HUGE. I have a little grasshopper phobia. I always think they'll bite me and poison/infect me with something. Yes, I know they don't have anything poisonous or detrimentally infecting. It scares me when the hop or move suddenly. I can tolerate jumping spiders but not damned grasshoppers! Still, I can't deny that grasshopper was magnificent and beautiful looking. It seemed innocent for some reason. Any
Visual Novels I watched the anime variants of Clannad, Fate/Stay Night, and School Days. I liked all three and from what I infer, these anime were derived from visual novels (VN). One day, I was bored and intrigued and looked up the VNs for these games and they're pretty expensive compared to my usual 3DS game. I can understand this because they're usually Japanese imports. Anyway, VNs seem to be known for having H-content and some even go so far as to calling them H-games. Today, I tried out some certain (free) VN. I don't want to mention it because I don't want to be responsible for outright exposing people to H content. It is actually interesting but I haven't gotten to any H content yet (I know there are some because there's an option t