Tagged Questions
0
votes
1answer
98 views
Mathematica vs Wolfram Alpha integration results
When I insert the following integration command in wolframalpha:
...
4
votes
5answers
110 views
Find the second derivative of $e^{x^{3}}+7x$
$$e^{x^{3}}+7x$$
Here is what I have tried so far,
$$y'=(e^{x^{3}})'+(7x)'$$
$$y'=3e^{x^{2}}e^x+7$$
$$y'=3e^{x^{3}+x}+7$$
I am supposed to find the second derivative but I believe I have already made ...
16
votes
4answers
643 views
Wrong Wolfram|Alpha limit?
I have this function:
$$ f(x,y) = \frac {xy}{|x|+|y|} $$
And I want to evaluate it's limit when $$ (x,y) \to (0,0)$$ My guess is that it tends to zero. So, by definition, if:
$$
\forall \varepsilon ...
25
votes
4answers
706 views
A limit wrong using Wolfram Alpha
I want to calculate the following limit:
$$\displaystyle{\lim_{x \to 0} \cfrac{\displaystyle{\int_1^{x^2+1} \cfrac{e^{-t}}{t} \; dt}}{3x^2}}$$
For that, I use L'Hopital and the Fundamental Theorem ...
2
votes
2answers
133 views
(Wolframalpha) this shouldnt give x=50?
This is my problem:
I need x or y for the triangle area that forms between the vertical axis(y) and the function y=100+2x where the area is equal to 2500.
so I used for condition to the linear ...
1
vote
1answer
98 views
An integral evaluation
I tried my luck with Wolfram Alpha, with $p \in \mathbb{R}$
$$\int_{-\infty}^{\infty} \frac{x^p}{1+x^2} dx = \frac{1}{2} \pi ((-1)^p+1) \sec(\frac{\pi p}{2})$$ for $-1<p<1$, and doesn't exist ...
0
votes
2answers
304 views
a question about the sum of $ e^{ikx}$
I have a simple question.
Let $
S = \sum\limits_{k = 1}^n {e^{ikx} }
$ using the typical trick , we also have
$
S\left( {e^{ix} - 1} \right) = e^{i\left( {n + 1} \right)x} - e^{ix}
$ and if $
...
0
votes
1answer
153 views
Understanding a Wolfram|Alpha explanation on a simple integral
I'll probably kick myself when someone explains it, but I can't understand where the 1/12 comes from after the re-substitution of u? I thought it would be 1/3, but it clearly isn't. Why is that?
...
0
votes
1answer
4k views
Use WolframAlpha to compute the real Fourier series of a function
How can I use Wolfram|Alpha to compute the Fourier series (with real coefficients $a_0, a_n$ and $b_n$)? (The 'Fourier series' command seems to summon the complex series)
I.e. $f(x) = x + \pi$ for ...
2
votes
2answers
485 views
limit of $2^n/3^{n/2}$ as $n\to\infty$
$$ \lim_{n\to\infty}\frac{2^n}{3^{n/2}}$$
I used wolfram to get the limit as follows:
"lim n tends infinity 2^n/3^(n/2)".
And using L'Hospital's rule the result was:
...
2
votes
2answers
527 views
Comparing integral resolutions using Wolfram Alpha / Mathematica
Equations are in $\LaTeX$ format; I'm still trying to understand how MathJax works.
Given the following integral:
$\int_0^{+\infty } \frac{1}{x \sqrt{x}} \, dx$
I'm pretty sure that does not ...
