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Mathematics
Mathematics
Problem
A curve is given by the parametrisation
x
=
e
3
t
,
y
=
e
2
t
+
t
.
x=e^{3t},\qquad y=e^{2t}+t.
x
=
e
3
t
,
y
=
e
2
t
+
t
.
(i) Determine
d
y
d
x
\dfrac{dy}{dx}
d
x
d
y
in terms of
t
t
t
. (ii) Find the slope of the tangent when
t
=
0
t=0
t
=
0
. (iii) Write the equations of the tangent and the normal to the curve at
t
=
0
t=0
t
=
0
.
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