Why did Itachi not kill Sasuke but instead poked his head during their last battle that led to Itachi's death?  Was it because of the clan symbol behind him? Or because he loved him?
From the beginning of the series, even during his last moments, Itachi poked Sasuke's forehead as a way of showing affection and apologizing.  But is that the only reason? Did he perhaps try to transfer some knowledge or memories to Sasuke? Or is it simply unknown?
Is a differentiable function always continuous? Continuous Functions are not Always Differentiable. But can we safely say that if a function f(x) is differentiable within range $(a,b)$ then it is continuous in the interval $[a,b]$ . If so , what is the logic behind it ? Jenkins + git: "tell me who you are" error, why does it need to tag? Why can a discontinuous function not be differentiable? I don't really understand why a discontinuous function cannot be differentiable.  In Stewart's Calculus, the definition of a function $f$ being differentiable at $a$ is that $f'(a)$ exists. Earlier it gives the definition of the derivative as $f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. It also has a theorem that if $f$ is differentiable at $a$, then $f$ is continuous at $a$. There is also a definition that a functions $f$ is continuous at a number $a$ if $\lim_{x\to a}f(x)=f(a)$.  Take for example the very simple function:  $$ f(x)=\begin{cases} x+1 &amp; x\geq0, \\ x &amp; x&lt;0.  \end{cases} $$  It is discontinuous at $x=0$ (the limit $\lim_{x\to 0}f(x)$ does not exist and so does not equal $f(0)$), but if I find the derivative using the limit above, I get the left and right limits to equal $1$. So therefore, the derivative exists.  According to the book, the function shouldn't be differentiable at $x=0$ as it has a discontinuity (continuity is a necessary condition of differentiability). What am I doing/understanding wrong? How many solutions has the equation $\sin x= \frac{x}{100}$ ? find a $\int_{x}^{g(x)} f(t)\,dt = 1$ Let $f : [0, 2] → \mathbb{R}$ be a continuous, positive function and  $$\int_{0}^1 f(x)\,dx = \int_{1}^2 f(x)\,dx= 1$$ For each $x \in [0, 1]$, prove that there exists a unique function $g(x) \in [1, 2]$ such that $$\int_{x}^{g(x)} f(t)\,dt = 1$$ and $g \in C^1$. Well, I think in $g(x) = x +1$, but I'm not sure. Any hint is appreciated.  Thank you. I'm very new to the GIS world, so my problem could be very stupid, but I'm going to try anyway.  Objective  Given a list of coordinates in longitude/latitude, stored as a .csv file, I want to create a buffer with distance of x km around those coordinates. (In case this is relevant, these coordinates are locations of the societies in the . These societies scatter all around the world.)  Problem  I'm only able to create buffers with distance in radial degrees, but I want to do them in (kilo)meters. I'm aware of the following Q&amp;A's, but following what's suggested therein doesn't seem to solve my problem:          What I have tried...   I start QGIS (v2.4), and Add delimited text layer  choose my .csv file and the x/y fields, click OK select WGS 84 as my CRS (also tried NAD83 but didn't make a difference), click OK right-click on layer and select Save As..., in the dialog box, choose the following and click OK:  add sccs_meter.shp as layer to the current project Select Vector > Geoprocessing Tools > Buffers > set buffer distance as 10   The result is a buffer with radius of approximately 1068km, which suggests that buffer distance is 10 degrees rather than 10 meters.  What did I do wrong here? Proving that the difference of the terms of a sequence, multiplied by $n$ converge Square root of Positive Definite Matrix When rolling percentages, do 1d100 and two d10s (percentiles) share the same probabilities? The state postulate is as follows: The state of a simple compressible system is completely specified by two independent, intensive properties. My first question is whether there is any justification for this postulate or whether it is simply an empirical law? That is, why is it not the case that 3 intensive variables are required to fix the state or even 4? If it is an empirical law with no justification and just happens to be a law our universe abides by, then why is it not one of the laws of thermodynamics as it clearly provides foundational value to the field of thermodynamics? My second question pertains to how we can know whether 2 intensive variables are in fact independant. Say temperature $T$ and specific volume $v$ for example. If we are given a thermodynamic problem, how would we know whether these are independent or not? or perhaps specific internal energy $u$ and pressure $P$. Are there certain combinations that are simply always independent of each other or does independence between intensive variables vary from problem to problem and require a full understanding of the problem at hand? Let us take a phase change for example. From my understanding of phase changes, I know that the boiling temperature is dependent on the pressure and hence I won't be able to use $T$ and $P$ as 2 variables to completely specify the state. But how would I know know what combinations of intensive variables will be independent in this case or any other case for that matter? Does it simply require rote memorization of all independent pairs of intensive variables for all thermodynamic problems or is there a more simple way to figure out what is independent and what isn't? I hope this question makes some sense and any help would be most appreciated! With a macro such as:  \def\naive{na\"{\i}ve}   I find that the space which I would hope to follow it, is absent. So, with  the \naive approach   I get     the naïveapproach   in the output. How do I bring back the space? I am trying to use a MERGE statement to insert or delete rows from a table, but I only want to act on a subset of those rows. The documentation for MERGE has a pretty strongly worded warning:     It is important to specify only the columns from the target table that are used for matching purposes. That is, specify columns from the target table that are compared to the corresponding column of the source table. Do not attempt to improve query performance by filtering out rows in the target table in the ON clause, such as by specifying AND NOT target_table.column_x = value. Doing so may return unexpected and incorrect results.   but this is exactly what it appears I have to do to make my MERGE work.  The data I have is a standard many-to-many join table of items to categories (e.g. which items are included in which categories) like so:  CategoryId   ItemId ==========   ====== 1            1 1            2 1            3 2            1 2            3 3            5 3            6 4            5   What I need to do is to effectively replace all rows in a specific category with a new list of items. My initial attempt to do this looks like this:  MERGE INTO CategoryItem AS TARGET USING (   SELECT ItemId FROM SomeExternalDataSource WHERE CategoryId = 2 ) AS SOURCE ON SOURCE.ItemId = TARGET.ItemId AND TARGET.CategoryId = 2 WHEN NOT MATCHED BY TARGET THEN     INSERT ( CategoryId, ItemId )     VALUES ( 2, ItemId ) WHEN NOT MATCHED BY SOURCE AND TARGET.CategoryId = 2 THEN     DELETE ;   This appears to be working in my tests, but I am doing exactly what MSDN explicitly warns me not to do. This makes me concerned that I will run into unexpected problems later on, but I cannot see any other way to make my MERGE only affect rows with the specific field value (CategoryId = 2) and ignore rows from other categories.  Is there a "more correct" way to achieve this same result? And what are the "unexpected or incorrect results" that MSDN is warning me about? Is it possible to remove a user's password using the net command?  I tried "net user &lt;name&gt; *" and just hitting return twice, but this does not work as expected. Is there any other way to do this? (I'd gladly take non-net commands, as long as they are built-in in XP SP3).  Edit: Seems, I did not make my intention clear. I don't just want to change the password, but remove it completely (so that the user may log in without having to supply a password).  I'm familiar with the "net"-reference and have searched online for several hours, but could not find a hint on how to do this. Capturing Blue Screen of Death (BSOD) screen Possible Duplicate:          Sometimes I get a BSOD screen for a split second and I have no chance to see the cause of it. It also happens when I am not at the computer. The event log doesn't have enough information. Is there a way or tool that captures the screen when it happens so I can look at the cause later.  I already did a memory diagnostics test so that's not the problem. Evaluation of $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7} = $$   $\bf{My\; Try::}$ I have solved Using Direct formula::  $$\sin \frac{\pi}{n}\cdot \sin \frac{2\pi}{n}\cdot......\sin \frac{(n-1)\pi}{n} = \frac{n}{2^{n-1}}$$  Now Put $n=7\;,$ We get   $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7}\cdot \sin \frac{4\pi}{7}\cdot \sin \frac{5\pi}{7}\cdot \sin \frac{6\pi}{7}=\frac{7}{2^{7-1}}$$  So $$\sin \frac{\pi}{7}\cdot \sin \frac{2\pi}{7}\cdot \sin \frac{3\pi}{7} =\frac{\sqrt{7}}{8}$$  Now my question is how can we solve it without using Direct Formula, Help me  Thanks How do I calculate the CRC32 (Cyclic Redundancy Checksum) of a string in .NET? How long do black olives last once opened? I opened a can of sliced black olives for my pizza and only used half. I put the leftovers into a sealed container with the liquid and put it in the fridge. Under those conditions how long will the olives last? Is there a better way to store leftover olives? How to Store Fresh Herbs interpreting scatter plots I have plotted my predictors versus my response variable in order to be able to fit a good Poisson model to my data. However i am getting  those scatter plots for nearly all predictors which make me rather worried since including these predictors is making my residual deviance a value of 575 on 571 df(high enough) Thanks Using Perl to change the url homepage for Internet Explorer