solve x e^H-x^2L=2 e^H-x^2L
Input interpretation :
2
x ã-x ‡ 2 ã-x
solve
2
Result :
x‡2
Plot:
2.0
1.5
1.0
0.5
2
ã-x x
-1.5
-1.0
-0.5
0.5
1.0
1.5
2
2 ã-x
Number line:
1.4
1.6
1.8
2.0
2.2
2.4
2.6
Generated
by Wolfram|Alpha
(www.wolframalpha.com)
onJuly22,2011 fromChampaign,
IL.
© WolframAlphaLLC—A Wolfram Research Company
1
diff x e^H-x^2L when x = 1
Input interpretation :
¶I x ã-x M
2
¶x
where x ‡ 1
Result :
-
1
ã
» - 0.367879
Plot:
1.0
0.8
0.6
0.4
0.2
-1
-0.2
-0.4
H x from -1 to 3L
1
2
3
Generated
by Wolfram|Alpha
(www.wolframalpha.com)
onJuly22,2011 fromChampaign,
IL.
© WolframAlphaLLC—A Wolfram Research Company
1
int x e^H-x^2L from 0 to 1
Definite integral :
1
-x 2
à xã
âx ‡
0
ã- 1
2ã
» 0.31606
Visual representation of the integral :
0.4
0.3
0.2
0.1
0.2
0.4
0.6
0.8
1.0
-0.1
Generated
by Wolfram|Alpha
(www.wolframalpha.com)
onJuly22,2011 fromChampaign,
IL.
© WolframAlphaLLC—A Wolfram Research Company
1