If $\lim_{x\to c}f'(x)=A$ then $f'(c)=A$
Prove that $f'(a)=\lim_{x\rightarrow a}f'(x)$.
How to copy a dictionary and only edit the copy Convert date to another timezone in JavaScript The first and (the) second chapter(s) are difficult - which is correct? I'm a little confused about the following sentences. Could you please tell me which one(s) is/are correct?        The first and the second chapter are difficult.   The first and the second chapters are difficult.   The first and second chapters are difficult.   The first and second chapter are difficult.      I believe #1 &amp; #3 are correct, while #2 &amp; #4 are incorrect.  But when seeing the answers to the Quora question , I wonder why they say #2 is correct. English (other than American English) has a clear differentiation between the two words. Both are about translocating something. In "bring" the something of somebody is moved to where the speaker is currently situated. "Take" is used to translocate something or somebody to a place that the speaker is not currently at.   You cannot “bring” your books to school if you are currently at home. You can only take them to school. Most of the time one can get the meaning from the context of the sentence but it can get very confusing when the other party is on the telephone and you do not know their location.   Why does American English not differentiate and when did it lose the differentiation? I have an account on Stack Exchange but when I try to login to  I do not see the option Login with Stack Exchange.       Why is this option now not available? This question was triggered by .  Basically, it goes like this: If you have a weapon with a certain magical effect, let's say the minor property unbreakable (can not be broken, requires special means) or temperate (no harm in temperatures between -20 to 120 F), it can bypass the immunity of something like a Werewolf because it is magical instead of mundane. This goes for any minor property because those properties are under the Magic Items portion of the DMG on pg.143.  How does this differ from a pair of gauntlets with the exact same effect being used as an improvised weapon (emphasis added for clarity) from dealing damage in the same manner to the same Werewolf? Or something that's clearly not a weapon like a Shield of Missile Snaring being used to bash an opponent? Sounds of the letter a How can I know, precisely, when to differentiate the sounds of the letter a, like in: apple and vault? This is Exercise 26 from Chapter V Algebraic Extensions in Lang's Algebra.  $F$ is finite normal extension over $k$ and $f(x)$ is irreducible in $k[x]$. If $f(x)=g(x)h(x)k(x) \in F[x]$ where $g(x),h(x)$ are monic irreducible factors in $F[x]$, I need to show that there exists an automorphism of $F$ which takes $g(x)$ to $h(x)$.  Any hints would be appreciated.  Sending one root to another is okay but how to do that for a collection of roots? Does $k+\aleph_0=\mathfrak{c}$ imply $k=\mathfrak{c}$ without the Axiom of Choice? Remove Sender name ( not email address) from outgoing Mac Mail Does any test actually prove causation? How do I specify unique constraint for multiple columns in MySQL? $\LaTeX$ and Mathematica z-score and Normal Distribution Every planar graph has a vertex of degree at most 5. I am trying to prove the following statement, any help!?     Prove that every planar graph has a vertex of degree at most 5. Considering the three types of Devil Fruits that has been explained are 1. Paramecia Type - where the user can get super human abilities and change their body parts into weapons, etc. 2. Zoan type - where the use can turn into a particular animal and inherit its abilities 3. Logia Type - where the user's body inherits a particular element and the body becomes like air which cannot be touched or damaged by non Haki users.  So what exactly is the type of Gomu Gomu no Mi? It cannot be Zoan or Logia. It's very close to a Paramecia but still doesn't have a logical explanation to be of Paramecia type! So is it some special type of Devil Fruit? Minecraft Test If A Chest Contains An Item I've seen a lot of questions for finding specific items in chests using commands using testforblock but how would you test if any block/item has been placed in a chest?  Thanks $\sum_{n=1}^\infty \frac{i^n}{n}$ converge? Is it possible to have connecting loop lines (like algorithm2e) in algorithmic? I am using the algorithmic package to typeset an algorithm. I would like to have connecting lines between the beginning and end of a loop or conditional like in the algorithm2e package. Is there an easy way to accomplish this, or am I better off switching to algorithm2e? PGFplots foreach equivalent to TikZ's with multiple variables separated by a slash