Evaluate
lim
x
→
0
e
−
3
x
3
−
1
+
3
x
3
−
9
2
x
6
14
x
9
\displaystyle \lim_{{{x}\to{0}}}{\frac{{{e}^{{-{3}{x}^{{3}}}}-{1}+{3}{x}^{{3}}-{\frac{{{9}}}{{{2}}}}{x}^{{6}}}}{{{14}{x}^{{9}}}}}
x
→
0
lim
14
x
9
e
−
3
x
3
−
1
+
3
x
3
−
2
9
x
6
Hint: Using power series.
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\displaystyle
Enter your answer as a number (like 5, -3, 2.2172) or as a calculation (like 5/3, 2^3, 5+4)
Enter DNE for Does Not Exist, oo for Infinity