Compute the Gradient at the Origin and Show That It Is Continuous at the Origin

You know, do you not, that $|x|^p= (x_1^2 x_2^2 cdots x_n^2)^p/2$? The gradient of a function of $n$ variables is the $n$-dimensional vector whose $i$th component is the derivative of that function with respect to $x_i$.

1. What is the origin of the word "yeet"?

As far as I can tell it's pure onomatopoeia - an exclamation combining exertion and triumph, as when making a winning basketball shot.Some here have tried to connect it with "yet"; I am not convinced on any such link. It's just a noise.It's also unclear to me how it became the name of a dance, though there's a lot on the history of that ("Li'l Meatball" etc) in other answers here.

2. What is the origin of the word 'behoove'?

From the Old English word behfian, related to the Old Frisian word bihvia and the Middle Low German behven, meaning "to have use of or need of"

3. origin of the name LANGHAM?

Langham English: habitational name from any of various places so called. Most, as for example those in Dorset, Norfolk, Rutland, and Suffolk, were named from Old English lang 'long' ham 'homestead', 'enclosure'; but one in Essex is recorded in Domesday Book as Laingaham, from Old English Lahhingaham 'homestead of the people of Lahha', and one in Lincolnshire originally had as its second element Old Norse holmr 'island'. Hope this helps.

4. What is the origin of Ganapathi Atharvasheersh?

The Ganapati Atharvashirsha Upanishad, AKA the Ganesha Upanishad or Ganapati Upanishad, is a text which claims to be an Upanishad associated with the Atharvana Veda; here is what it says about itself in verses 16-18 (see pages 5-7 of this PDF file): The last sentence is where it gets the name Atharvashirsha, or "head of Atharva", because some interpret the line not as an introduction of a quote as this translation renders it, but rather as a statement that the text as a whole was said by the sage Atharva, i.e. that it came right from the head of Atharva.Now having said that, it should be noted that the Ganapati Atharvashirsha Upanishad is widely considered to be a later interpolation, not a genuine Upanishad of the Atharvana Veda. This is for multiple reasons. First of all, references to Ganesha in ancient Hindu scripture are few and far between, as Ganesha rose to popularity much later. But more importantly, it's not listed in the Muktika, the canonical list of Upanishads, which means that it's presumably less than 400 years old. Let me explain why.Hindu scripture was passed down via oral tradition, and there were some good oral tradition processes and some bad ones. An example of an incredibly rigorous oral tradition process is the one used to preserve the Samhitas of the Vedas, the core part of the Vedas whose verses were heard directly from the gods. Because these verses were of divine origin, people took great pains to preserve every last syllable exactly, such as parallel disciplic successions and independent cross-checks. That is how scholars are so sure that, e. g. the Rig Veda Samhita as we have it today is almost the exact same document that the sage Vyasa compiled.But other texts were not so rigorously prserved. In particular, the Muktika Upanishad, a text listing the names of the Upanishads of each the Vedas, was passed down with so little rigor that anyone in the disciplic succession could freely add in titles of Upanishads as he saw fit. This was not done maliciously; it was just students innocently thinking that the text they had received was incomplete, since they were aware of supposed Upanishads which were not mentioned. This is how Upanishads that are now widely considered to be spurious, like the Kali Santarana Upanishad as I discuss in this question, were added onto the Muktika canon. The text of the Muktika only started becoming stable once it was committed to writing, but that was only in the seventeenth century. So the Muktika is basically a list of all the documents that people even remotely considered to be an Upanishad up until the seventeenth century.Yet the Ganapati Atharvashirsha Upanishad is not even listed in the Muktika Upanishad, which you can read here. That means that none of the students in the disciplic successions, going all the way up to a few hundred years ago, ever added it to the text, which means that they presumably had not heard of it. So that implies that origin of the text, or at least the time when it started being considered an Upanishad, was newer than when the Muktika Upanishad was committed to writing