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masters

Active member
Jan 30, 2012
13
icu.jpgblogs.jpgmagnum pi.jpgScienceTeachers.jpgloveformula.jpg
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780

dwsmith

Well-known member
Feb 1, 2012
1,673
We do get a full heart. See W|A.
Not on the actually version of Mathematica. I used implicit plot, contour plot, and regular plot with the plus and minus square root. Only half.
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
Not on the actually version of Mathematica. I used implicit plot, contour plot, and regular plot with the plus and minus square root. Only half.
Note that $\sqrt[3]{x^2}$ is not the same as $x^{\frac 2 3}$.
With the latter, you'd only get half a heart (since it is not defined for negative numbers).
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Note that $\sqrt[3]{x^2}$ is not the same as $x^{\frac 2 3}$.
With the latter, you'd only get half a heart (since it is not defined for negative numbers).
Do you mean that $ x^{\frac{2}{3}}$ is not defined for negative numbers ?
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,780
Do you mean that $ x^{\frac{2}{3}}$ is not defined for negative numbers ?
There are different definitions for $x^{\frac{2}{3}}$.
Different choices for its domain can be made.
For instance $x^\alpha$ where alpha is a positive real number, is only defined for $x \ge 0$.

More to the point, calculators cannot calculate $(-1)^{0.6667}$ as a real number.
And they usually do not have exceptions for the special case where the power is a whole numbered fraction with an odd denominator, which is the only case where $x^\alpha$ can be defined for negative x.