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mathematics

mathematics

Using $\lim\limits_{x \to 0} \frac{\sin x}{x} = 1$ evaluate the limit

Use $$\lim_{x\to 0} \frac{\sin x}{x} = 1$$ to evaluate the limit $$\lim_{x\to 0} \frac{x\tan (x^2)}{\cos(3x)\sin^3(2x)}$$ I'm really not sure how to go about this apart from trig identities and

mathematics

Plural of "the [x] of [y]"

What is the proper usage between 1) and 2)? 1) "Determine the values of the coefficients." 2) "Determine the value of the coefficients." Each coefficient has one value in this cont

english-language

Limit $\lim_{x \to 0}\frac{\sin(x^2-x)}{x^2-\tan x}$ without l'Hospital

$$\lim_{x \to 0}\frac{\sin(x^2-x)}{x^2-\tan x}$$ I could not solve this without l'hospital.

mathematics

Evaluate $\lim _{x\to \infty }\left(\sqrt{4x^2+x}-\sqrt{4x^2-1}\right)$

The task is: Evaluate $\lim _{x\to \infty }\left(\sqrt{4x^2+x}-\sqrt{4x^2-1}\right)$ Can it be solved without using L'Hospital's rule? If so, what should I use?

mathematics

What word describes the opposite of 'elevated'?

Assume things are graded in some way and some level is assigned the attribute 'normal'. Things which stay (always) above this level are called elevated (relative to the norm). Things which st

english-language

How long Saber has been waiting for Shirou after she's died?

Regarding to the question that was asked before: Do Emiya Shirou and Arturia ever meet again after Fate/stay night? In the Visual Novel of Fate Stay/Night Realta Nua once you have seen all 5 ...

anime

im having trouble finding a specific anime i have seen in the past

it was a school romance the main girl was short with brown/blond hair and a big for head the main guy was tall with dark hair he had been going out with a model i think since middle school but was ..

anime

A manga about a loner guy that helps an animal girl

I read a manga that was about a loner guy that meets and eventually helps an animal girl. I believe that she is wolf/lion like. As the story progressed the events and the beast girl helped the loner .

anime

How does UUB is related to Maitibu?

Dragon Ball fans out there, please explain how does goku say UUB is related Maitibu. Please solve my childhood mistery.

anime

looking for a anime to watch? [on hold]

i am looking for an anime with a girl as a main character ....romance ...i dont want ecchi ...i want a strong female ...mayby the story is in high school ...it doesn't have to be all about romance...

anime

Difference between Lost Technica 《秘奥義{ロスト・テクニカ}》 and Last Crest 《魔道極法｛ラスト・クレスト}》?

The terms Lost Technica 《秘奥義{ロスト・テクニカ}》 and Last Crest 《魔道極法｛ラスト・クレスト}》 are quite ambiguous, since they are usually mentioned together with the

anime

Evaluate $\lim\limits_{x\to 0}\dfrac{\sin (x) - x}{\tan(x)-x}$

$$\lim\limits_{x\to 0}\dfrac{\sin (x) - x}{\tan(x)-x}=?$$ I got $-\dfrac12$ using L'hopital. Is there a way to work this without using l'hopital/taylor series/derivatives ?

mathematics

A positive integer with is not a perfect square is a product of distinct prime factors

This was used as part of the explanation for the following question, but I don't see why it is true. How to understand Apostol&#39;s proof of the irrationality of $\sqrt{n}$ if $n$ is not a

mathematics

Is it (theretically) possible to reduce inertial mass without reducing matter quantity?

Ok, please bear with me because I only have a very little (or no?) understanding of physics outside Newtonian laws... So I was playing a video game called "Mass Effect" in which a particular

physics