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• Today, 10:37
I substituted $n=\frac 1{x^2}$, which also means that $x^2=\frac 1 n$. So we get $\Big(1 + \frac 32 x^2\Big)^{1/x^2} = \Big(1 + \frac 32 \cdot \frac... 7 replies | 82 view(s) • Today, 09:14 It's like this: $$\Big(1-\frac 12 x^2 + \ldots\Big)\Big(1+\frac 12 (2x)^2 - \ldots\Big)\\ =1\cdot 1 -\frac 12 x^2 \cdot 1+1\cdot \frac 12 (2x)^2 -... 7 replies | 82 view(s) • Today, 07:04 The series expansion of \cos x = 1 - \frac 12x^2 + \ldots. And the expansion of \frac 1{1-x} = 1+x+x^2+\ldots So:$$\frac{\cos(x)}{\cos(2x)}... 7 replies | 82 view(s) • April 2nd, 2020, 12:25 Klaas van Aarsen replied to a thread f in Calculus It appears the answer is: dkm Acronym for "don't kill me". Often used when somebody says something that somebody else finds really funny,... 5 replies | 162 view(s) • April 2nd, 2020, 11:56 topsquark replied to a thread f in Calculus I believe the proper question is "What the 'f'?" -Dan 5 replies | 162 view(s) • March 31st, 2020, 17:53 topsquark replied to a thread [SOLVED] 299What is the acceleration in Calculus Wait! What do you mean by you changed it to v(t)? The particle's position is x(t) = sin(t) - cos(t) means that v = \dfrac{dx}{dt}. You can't just... 4 replies | 130 view(s) • March 30th, 2020, 05:31 Let's take a look at a couple of examples. If$f(x)=x$, then$f'(x)=1$and$f''(x)=0$. So$\lim\limits_{x\to +\infty}f'(x)\ne 0$, isn't it?... 21 replies | 404 view(s) • March 30th, 2020, 04:26 Yep. (Nod) And no, nothing more specific. 21 replies | 404 view(s) • March 30th, 2020, 03:32 I believe so yes. Consider$f(x)=\ell$. It satisfies all conditions, doesn't it? (Wondering) And it is monotone instead of strictly monotone. To... 21 replies | 404 view(s) • March 29th, 2020, 14:38 Indeed. (Thinking) 21 replies | 404 view(s) • March 29th, 2020, 14:26 Yep. (Nod) 21 replies | 404 view(s) • March 29th, 2020, 13:57 Then the inequality also holds yes. What if fill in, say,$f'(y)=-1$in the inequality? Would it satisfy it? (Wondering) 21 replies | 404 view(s) • March 29th, 2020, 13:19 That is a possibility yes. What happens if$f'(y)$is negative? (Wondering) 21 replies | 404 view(s) • March 29th, 2020, 13:08 We have an expression with$f(y)$,$f'(y)$, and$\ell$. And we already know that$\ell\in\mathbb R$, don't we? So it can't be$\pm\infty$either. ... 21 replies | 404 view(s) • March 29th, 2020, 10:27 Ah okay. But that is not the case now is it? (Wondering) Sounds like a plan. (Nod) 21 replies | 404 view(s) • March 29th, 2020, 08:35 Let's see, suppose we pick a convex function, say$f(x)=x^2$. It's convex isn't it? Does$\lim\limits_{x\to +\infty}f'(x)$exist? (Wondering) ... 21 replies | 404 view(s) • March 29th, 2020, 07:38 Hey mathmari!! Let's start with: It follows from$\lim\limits_{x\rightarrow +\infty}f(x)=\ell$that$\lim\limits_{x\to +\infty}f'(x)=0$... 21 replies | 404 view(s) • March 26th, 2020, 20:42 Have you tried looking at \lim_{n \to \infty} \dfrac{a_{n + 1}}{a_n}? -Dan 2 replies | 74 view(s) • March 26th, 2020, 18:35 Let y'(x) = v(x). Then your equation becomes v'(x) + v(x) = -F(x) Now you have a first degree linear ordinary differential equation. You can't... 1 replies | 71 view(s) • March 25th, 2020, 17:42 Yep. (Nod) I'd say 'and this is confirmed...' rather than 'since this is confimed...' though. (Emo) 12 replies | 382 view(s) • March 25th, 2020, 15:50 Ah good. (Whew) Does the solution for$x$match the given general solution? (Wondering) 12 replies | 382 view(s) • March 25th, 2020, 15:40 How did you get$x_{1}=\frac{1}{3}$? (Wondering) 12 replies | 382 view(s) • March 25th, 2020, 15:06 Don't we have$x_2=h(y)$so that$f(x_2)=f(h(y))=y$? And therefore$g(f(x_2))=g(y)=x_1$? (Wondering) 4 replies | 145 view(s) • March 25th, 2020, 14:35 Suppose it is correct, then what are the solutions of$Ax=\begin{bmatrix}1\\3\end{bmatrix}$? (Thinking) 12 replies | 382 view(s) • March 25th, 2020, 14:33 Hey mathmari!! How about a proof by contradiction? That is, suppose$g\not\equiv h$, then there must be an$y\in B$such that$g(y)\ne h(y)$,... 4 replies | 145 view(s) • March 25th, 2020, 14:13 Since we should get the same$A$regardless of the value of$\lambda$, I think that for instance$a_{12}$must be$0$. (Thinking) 12 replies | 382 view(s) • March 24th, 2020, 15:20 Hey evinda!!$A$is a fixed matrix, isn't it? It shouldn't depend on$\lambda$should it? (Worried) The lambda is only supposed to describe... 12 replies | 382 view(s) • March 23rd, 2020, 06:48 Well, to be fair, this is not immediately obvious. (Worried) Let's take a slightly different angle. According to the wiki page about matrix... 3 replies | 209 view(s) • March 23rd, 2020, 03:44 Hi Peter, Capital Tau is just a T. Mathjax doesn't have a caligraphic Tau, but the caligraphic T is the same thing:$\mathcal{T(S)}\$....
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1. Hi, pls help me to solve for x, 2^x =8x. Thanks.
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