Articles of wolfram alpha

A WolframAlpha error?

Consider the equation: $$ \dfrac{1}{\sqrt[3]{(x+3)^2}}-\dfrac{1}{\sqrt[3]{x^2}}=0 $$ that has the solution $x=\dfrac{-3}{2}$ as can be easely verified. But WolframAlpha gives no solutions (here). Someone knows why? Or I have some stupid error?

Parametrization of curve

I need to find parametrization of $(1+x)y^2=(y+2x)x$. I tried to put all $x$-s on one side, and all $y$-s on other but that can’t be done. Could someone please help? Thanks.

The last few digits of $0^0$ are $\ldots0000000001$ (according to WolframAlpha).

Can anybody explain how this comes about?

Tell Wolfram Alpha that a variable is a natural number

How can I tell Wolfram Alpha that some variables are natural numbers, when I want to solve a equation? An example of what I want to do: $\binom{n}{k}\cdot p^k \cdot (1-p)^{n-k} = \frac{1}{\sqrt{n\cdot p \cdot (1-p)}}\cdot \frac{1}{\sqrt{2 \cdot \pi}} \cdot e^{-\frac{1}{2} \cdot \left(\frac{x-np}{\sqrt{n \cdot p \cdot (1-p)}}\right)^2}$ solve for $x$ with $n,k \in \mathbb{N}$, $0 […]

Infinity times $i$

Wolfram Alpha says: $$i\lim_{x \to \infty} x = i\infty$$ I’m having a bit of trouble understanding what $i\infty$ means. In the long run, it seams that whatever gets multiplied by $\infty$ doesn’t really matter. $\infty$ sort of takes over, and the magnitude of whatever is being multiplied is irrelevant. I.e., $\forall a \gt 0$: $$a\lim_{x […]

cubic root of negative numbers

Excuse my lack of knowledge and expertise in math,but to me it would came naturally that the cubic root of $-8$ would be $-2$ since $(-2)^3 = -8$. But when I checked Wolfram Alpha for $\sqrt[3]{-8}$, real it tells me it doesn’t exist. I came to trust Wolfram Alpha so I thought I’d ask you […]

Wrong Wolfram|Alpha limit? $ f(x,y) = \frac {xy}{|x|+|y|} $ for $(x,y)\to(0,0)$

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: $$ \forall \varepsilon \gt 0, \exists \delta \gt 0 \diagup \\ 0\lt||(x,y)||\lt \delta , \left|\frac{xy}{|x|+|y|}\right| \lt \varepsilon $$ Then $$ \lim_{(x,y)\to(0,0)}\frac […]

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 of Calculus, obtaining the following: $$\displaystyle{\lim_{x \to 0} \cfrac{\displaystyle{\int_1^{x^2+1} \cfrac{e^{-t}}{t} \; dt}}{3x^2}}=\displaystyle{\lim_{x \to 0} \cfrac{\frac{e^{-(x^2+1)}}{x^2+1} \cdot 2x}{6x}}=\lim_{x \to 0} \cfrac{e^{-(x^2+1)}}{3(x^2+1)}=\cfrac{e^{-1}}{3}$$ But if I calculate the limit in Wolfram Alpha, I get the […]

WolframAlpha says limit exists when it doesn't?

I was trying to calculate the following limit: $$ \lim_{(x,y)\to (0,0)} \frac{(x^2+y^2)^2}{x^2+y^4} $$ and, feeding it into WolframAlpha, I obtain the following answer, stating the limit is $0$: However, when I try to calculate the limit when $x = 0$ and $y$ approaches 0, the limit is 1… Is the answer given by WolframAlpha wrong? […]