Start from standard expansion of Calculus for = 1 + t + + + . . . (1)
Substitute one time t = x^2 into expansion (1) to get
e^(x^2) = 1 + x^2 + + + . . . (2)
Substitute next time t = x^3 into expansion (1) to get
e^(x^3) = 1 + x^3 + + + . . . (3)
Subtract (3) from (2). You will get
e^(x^2) - e^^(x^3) = x^2 - x^3 + the terms of the converging series with degrees of "x" higher than or equal to 4.
Therefore
= 1 - x + the terms of the converging series with degrees of "x" higher than or equal to 2. (4)
Thus, when you take the limit at x--> 0 of , you will get . ANSWER
The rest of the terms contribute 0 (zero) to this limit.
Solved.
------------------
I wrote this post, because arguments of @MathLover1 are I N V A L I D.
Had I answered this question as @MathLover1 did it, with expressions on the way, I would loose my reputation FOREVER
in the eyes of my teachers.
