• Today, 15:25
It's a "rite of passage" for calculus students. (Smile)
3 replies | 22 view(s)
• Today, 14:49
Hi brynjolf23 and welcome to MHB! I've placed the appropriate delimiters around your LaTeX code. They are (for this site) \$...\$ - for inline...
1 replies | 17 view(s)
• Today, 13:05
Well, I can see that we have $$\text{something}=\frac{1}{\text{something irrational}}\implies\text{ something is irrational}$$ Correct? How...
8 replies | 109 view(s)
• Today, 12:48
Right. So what that means is that there is no angle $\alpha$ that specifically has $\sin\alpha=\frac 1n$ (rational) and also a rational...
8 replies | 109 view(s)
• Today, 12:15
I still don't see why what I wrote is incorrect. $c$ is irrational, so must be $\sin10^\circ$.
8 replies | 109 view(s)
• Today, 12:03
Those two answers only differ by a constant, because $\cot^2 x+ 1 = \csc^2x$.
3 replies | 22 view(s)
• Today, 11:48
It holds for $\alpha=\arctan(3/4)$ because $(3,4,5)$ is a Pythagorean triple. The point is that there is no such triple having $1$ as one of its...
8 replies | 109 view(s)
• Today, 09:04
By that logic that would hold for any angle, wouldn't it? But it doesn't, since with $\alpha=\arctan(3/4)$ both $\cos\alpha$ and $\sin\alpha$ are...
8 replies | 109 view(s)
• Today, 08:58
Not quite that simple! What that argument shows is that $\sin10^\circ$ and $\cos10^\circ$ cannot both be rational. In that case, there would indeed...
8 replies | 109 view(s)
• Today, 08:48
Could it be this simple? Consider right triangle $ABC$ with $\angle{A}=80^\circ$, $\angle{B}=10^\circ$ and $\overline{AC}=1$. Then...
8 replies | 109 view(s)
• Today, 07:20
l will now attempt to, explicitly, complete the demonstration that Df(a) v = \sum_{ 1 \le j \le n } v_j D_j f(a) \ \ \ \ (v \in \mathbb{R}^n ) ...
4 replies | 62 view(s)
• Today, 04:56
Let $x = \sin10^\circ$. The formula for $\sin3\theta$ shows that $3x - 4x^3 = \sin30^\circ = \frac12.$ So $8x^3 - 6x + 1 = 0.$ If $y=2x$ then $y^3 -... 8 replies | 109 view(s) • Today, 04:29 Yep. (Nod) 12 replies | 173 view(s) • Today, 02:23 Hi, Peter. Try dividing the first line of (2.11) through by$t$. Now take the limit as$t\rightarrow 0$, use the definition of directional... 1 replies | 40 view(s) • Today, 01:11 Here is an attempt to show Df(a) v = \sum_{ 1 \le j \le n } v_j D_j f(a) \ \ \ \ (v \in \mathbb{R}^n ) Now we have ... Df(a) v =... 4 replies | 62 view(s) • Today, 00:59 Thanks Country Boy ... ... appreciate the help ... Peter 4 replies | 62 view(s) • Today, 00:54 Thanks GJA ... that was really helpful ... Still reflecting on what you have said ... Thanks again ... Peter 2 replies | 60 view(s) • Yesterday, 23:26 Here is this week's POTW: Let$ABCD$be a convex quadrilateral with$\overline{AB}=\overline{AD}$. Let$T$be a point on the diagonal... 0 replies | 34 view(s) • Yesterday, 23:21 No one answered this weeks POTW...my solution follows: (a) Apply conservation of angular momentum (subscripts of$R$pertain to the rod, while... 2 replies | 149 view(s) • Yesterday, 22:33 greg1313 replied to a thread Integrals and Limits in Calculus Another way of looking at this is to visualize$\int_0^\infty c\,dx$, where$c>0$. Now make a drawing, including the$x$-axis, of what this integral... 12 replies | 173 view(s) • Yesterday, 22:03 Comparison is fine, but it must be a VALID comparison. The idea would be capsulized as "closer to zero". Bad Example: It is also true that for x... 3 replies | 69 view(s) • Yesterday, 18:27 Conceptually an integral corresponds to the area under a graph. If that graph extends to infinity, the height of the graph must approach zero, since... 12 replies | 173 view(s) • Yesterday, 18:06 Erm... then I'm not quite sure what I can use or not. Can you perhaps use the fact that a series$x_1 + x_2 + ...$can only converge if$x_n \to 0$?... 12 replies | 173 view(s) • Yesterday, 17:39 What is the regular/basic definition of limits that you are familiar with? The generic definition is the so-called$\varepsilon$-$\delta$... 12 replies | 173 view(s) • Yesterday, 16:37 The multiplicative inverse of q with respect to q'. That is, it is such that: $$_{q'}^{-1} \cdot q \equiv 1 \pmod {q'}$$ And since$q$and$q'$... 5 replies | 87 view(s) • Yesterday, 16:10 Suppose$\lim\limits_{x\to\infty} f(x)=c > 0$. Then for$\varepsilon = \frac c 2 > 0$there must be some$a$such that for every$x>a$we have that... 12 replies | 173 view(s) • Yesterday, 15:58 Hi, Peter. This question is perhaps a little deeper than it seems initially. The subtlety lies in the fact that$\phi_{a}(x)$is an... 2 replies | 60 view(s) • Yesterday, 15:36 Hey MermaidWonders! Let's start with$\int_0^{\infty} f(x)\,dx$, which must also converge. Then$\lim\limits_{{x}\to{\infty}}f(x) = 0\$ isn't it?...
12 replies | 173 view(s)
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