I study the following equation:
f[x_] := (Exp[2*x] - Log[E + x])/(x^3 + Sin[x]*Cos[x])
Plot[f[x], {x, -10, 2}]
When I observe the plot of this function, It seems that there is no problem on 0. However, the denominator of the function can not be nul.
Indeed, if I solve the following equation, i see that the denominator can be nul at 0.
NSolve[(x^3 + Sin[x]*Cos[x]) == 0, x, Reals]
May you give ideas about my misunderstanding? Is it because of Mathematica or do I make stupid mathematical mistakes ?
x -> 0
exists, and Mathematica is fine with that. DoLimit[f[x], x -> 0]
. $\endgroup$Plot
only samples your function at a finite number of points and in this case it never happens to evaluatef[0]
. Since the function is smooth near zero the adaptive algorithm doesn't see the issue. In the unlikely event it hits your limit point it is robust enough to ignore the single-point error. $\endgroup$