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Mathematics
Mathematics
Problem
Consider the curve defined by
x
=
e
t
x = e^{t}
x
=
e
t
and
y
=
t
e
t
y = t e^{t}
y
=
t
e
t
. Determine the equation of the tangent to the curve at the point where the slope is
5
5
5
. a)
y
−
5
e
5
=
5
(
x
−
e
5
)
y - 5e^{5} = 5\bigl(x - e^{5}\bigr)
y
−
5
e
5
=
5
(
x
−
e
5
)
b)
y
−
4
e
4
=
4
(
x
−
e
4
)
y - 4e^{4} = 4\bigl(x - e^{4}\bigr)
y
−
4
e
4
=
4
(
x
−
e
4
)
c)
y
−
4
e
4
=
5
(
x
−
e
4
)
y - 4e^{4} = 5\bigl(x - e^{4}\bigr)
y
−
4
e
4
=
5
(
x
−
e
4
)
d)
y
−
e
4
=
5
(
x
−
e
4
)
y - e^{4} = 5\bigl(x - e^{4}\bigr)
y
−
e
4
=
5
(
x
−
e
4
)
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