Beginner, help with Plot function

Questions
,
1

Hello,

I am trudging my way through my first Mathematica assignment for Calculus 1 and am loving the software, the things it can do is amazing. However, I am not running into an issue when I am trying to input this function into a graph using the Plot tool. I do not see where I am going wrong. Any help? :slight_smile:

Plot[x^2 - e^-x^2 == 0, {x, -10, 10}]Plot[x^2 - e^-x^2 == 0, {x, -10, 10}]

2

Assuming you meant “e” to be the euler-number, the correct syntax is,

(* One way of doing this. *)
Plot[x^2 - Exp[-x^2] == 0, {x, -10, 10} ]

(* Or...*)
Plot[x^2 - E^(-x^2) == 0, {x, -10, 10} ]
3

Syntax counts a bit, the Euler number is E in Mathematica or use function Exp[] as usual

Plot[x^2 - Exp[-x^2] == 0, {x, -10, 10}]

but what do you intend with it? Solving that equation symbolically would be

In[5]:= Reduce[x^2 - Exp[-x^2] == 0, x]


Out[5]= C[1] \[Element] 
  Integers && (x == -Sqrt[ProductLog[C[1], 1]] ||    x == Sqrt[ProductLog[C[1], 1]])

finding a root (there are 2) would be

In[6]:= FindRoot[x^2 - Exp[-x^2] == 0, {x, -1}]

Out[6]= {x -> -0.753089}

solving it graphically means to type

Plot[{x^2, Exp[-x^2]}, {x, -1, 0}, 
 Epilog -> {PointSize[Large], Red, 
   Point[{-0.7530891649796748, (-0.7530891649796748)^2}]}]
4

It is always the smallest things, isn’t it? It ended up being the mix-up between e and E, thanks so much for your help guys!