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Mathematics
Mathematics
Problem
Consider the curve defined by
x
=
e
3
t
x=e^{3t}
x
=
e
3
t
and
y
=
ln
(
5
t
2
)
y=\ln(5t^{2})
y
=
ln
(
5
t
2
)
. Evaluate
d
2
y
d
x
2
\dfrac{d^{2}y}{dx^{2}}
d
x
2
d
2
y
at
t
=
1
t=1
t
=
1
. a)
−
8
3
e
−
3
-\dfrac{8}{3}e^{-3}
−
3
8
e
−
3
b)
−
8
9
e
−
6
-\dfrac{8}{9}e^{-6}
−
9
8
e
−
6
c)
8
9
e
−
6
\dfrac{8}{9}e^{-6}
9
8
e
−
6
d)
−
2
9
e
−
6
-\dfrac{2}{9}e^{-6}
−
9
2
e
−
6
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