e^tcutus R.rr'eu t o(
[\Iaximum mark:
/(r) :
5] ffi
e3'. The line .L is the tangent to the curve of .f at
Find tlre equation of -L in the form A : mx: + c.
Let
Tk, s l-
(0, 1)
2.
fl\Iaximum mark:
Let
/(r) :
(u)
Sho'w
6] ffi
kt:3.
that the point P(2,84) lies on the crrrve of
At P, the normal to the curve is parallel to
(b)
/
[1]
y:l*.
6
Fincl the va,lue of k.
l5l
3
6] ffi
Consicler the curve A :
h,:r
[\,Iaxirnuni rnark:
e
IR..
c
I
-1
da
(u)
Fincl
(b)
Determine the equation of the normal to the crtrve at the point P(-2.4).
t21
dc
[4]
4
[I\,Iaximurn mark:
6] ffi
Let/(r) -pr3-qr. Ltr:0,thegladientof
find the vaiue ofp and
thecurveof
/is2.
Giventhat .f-1(12)--2,
q.
5
fNlaxirnum mark:
Let
/(r) :
6] ffi
ix2e'and 9(r) -- 4r
-
t:2.
(u)
Find //(o).
t3l
(b)
Find the n-coordiuate where the tangents of J@) and 9(r) are parallei.
t3l
6
[N,laxirnurn rnalk:
7] ffi
:6,
:2, s'(3):4 and h'(3) :
Find tlre equatiorr of the norrnal to the graph ol f af, :r :3.
Let f
7.
(r): s(r)h(t).
where e(3)
h(3)
1
6] ffi
Consicler the curve y::-+
5-r
fNilaximurn rnark:
-4.
r- I
Find thc r-coordinates of the points on the curve where the gradient is zero.
8.
H
ESt
flllaximum mark: 7j
Tlre values of the functions
the following table.
r
Lcth(c;)
/
and g and their derivatives for
.f
(r)
3
3
7
5
s@)
6
r :3
and
f'(r)
s'@)
-8
2
1
D
r:
7 arc shown in
:f(r)s@).
(u)
Find h(3).
(b)
Find the equation of the norrnal to h when
tel
L4l
r
:
7
t5l
9.
[lVlaxirnurn mark: 15]
Lct f(r)
,
: l:-2
-:-*3.
for
r > 2.
(u)
Write down the equatiot of the horizontal asvmptote of
(b)
Fincl
//(r).
:
ae-r
Let lz(r)
/.
t2l
l3l
t
b. The graph of
f
and h. have the same horizontal asl'6ptre6".
(") \Vrite down the value of b.
(d) Given that ht (2) : '-2e-2, firrd the valne of ci.
(") There is a value of r for which the graphs of /
Find tliis gradient.
l2l
t4l
ancl h have the sanre graclient.
l4l