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Mathematics
Mathematics
Problem
For
x
x
x
near
0
0
0
, consider the quotient
Q
(
x
)
=
e
3
x
−
1
−
3
x
e
2
x
−
1
−
2
x
.
Q(x)=\frac{e^{3x}-1-3x}{e^{2x}-1-2x}.
Q
(
x
)
=
e
2
x
−
1
−
2
x
e
3
x
−
1
−
3
x
.
(a) Verify that direct substitution of
x
=
0
x=0
x
=
0
yields an indeterminate form. (b) Determine
lim
x
→
0
Q
(
x
)
\displaystyle \lim_{x\to 0} Q(x)
x
→
0
lim
Q
(
x
)
and show all algebraic work required to arrive at the finite value.
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