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CHAPTER Answer y
the and
bx'
3r common
=
8x
(c)-3
for be
6(c)g(r)=
+ inflection y
x+
and
A,
R point 27x=4y
lines
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to
normal
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and is
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equal the straight
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then Let then
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,
Single Calculus5.2
(b)11. (a)6. 13. 12.
(c)1.
Correct f)=x= For (c)Y= V2(y= r+i
ax) Equation
the
functions andMultiple
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e)=ysinr² |2r+rsin -V2r+ =
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of
line
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(b, f"(2)=12f)=0
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Genga ing Correct
c)
13.
Answers
(a,
b)
14. Type x-axis
curve
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but axes
touches equal
it y is is
btcx 4a.
ar
= of
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at I; 2y
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b, 45° the the =
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to co-ordinate -a
x-axis cos
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touches
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curve
. 2/53
+ the
ty in
the
x=ar,
of
Derivatives (b) (-3)
(-2)
x=t3
the
x=tv3
(d) meets
+
bx
+
ax
for
x
alsoof
the
to
t+
=
y
and
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-1sxs| (d)
9
+
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linel
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U
abscissa
oo) curve 2/5 (d)
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(b) yform
0)(2, 1) are x> are =2t-
1(b)
gradient
contact
the xy (-, 4] pointby ratio
[3,
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x(2 curve divided3/2
(c)
(0, the tangents 3 (C) that the
= the pointthen
x
as of (b) any
y' parametrically
points so the at in
on of 0) is externally
atthe
gradient
equation
with
curve t to tangent
axes
1) (-1, negative parameter
5.1
DPP 2) -3) (1, Pis
-
(y (y
x=tN2
x=+V2
at then
tangent 3/8)(9/4,
(c)
point
a
the hasx>-1
(a) x<-1
1)
(1, the (b)
point between
2
represented
normal
is
2V43 of =0 (-4,4)
the
the (b)
(c) portion
3/4
contact
of between
P, (4,4)
(a) zero
has
d (c) value (1,4)
(a)
at at curve the
distance 9 1) interval of 1/4
(a)
theagain X-axis
(a) (c) If a8.If
From - Theay=point
the (a) The (a
7. 9. 10. 11.
parametrically
the the point horizontal
x function equations coordinates tangent
curve
of
at through value
5 this the
6x-7y-11=0
(b) is
inverse
3 both
-2t 1=0 at -1
passIine
(d) a same 3
(d) = l=0 the
4x+y-l=0
(d) If
has x 0. the are
Type curve
2r at by >
+y-
Normal
and
Tangent = c tangent 1
t +
the its a then
g(r)4y- parametrically 0)(2e, 0) which
(b) (l/e,
(d) are
CHAPTER Answer y
the and
bx'
3r common
=
8x
(c)-3
for be
6(c)g(r)=
+ inflection y
x+
and
A,
R point 27x=4y
lines
to 8 (d) y br² to (b) tE
to
normal
-
Correct =+3t
and is
b+c = + let tangent =+e,
equal the straight
y=tax and
a of
represented
at curve
the -8=0have+
-1=0 (b) l the 4x-y+|=0
is -6 +x+ 1=0 (c) x
a 1(b) fx)pointofb of the
y axisare
Singleof x is the
andof of of
by -1) function
a value equation and A to
equation
represented
3y 6y curves0) value + equation
P(2,+ 7x+ (-1, and = x-4yis. the point (a) 0)(e,
0)(1, (c)
normal
the the -2
tangent f(x) curveX=[+e
touches
point2r the pointthen(a)0 the (a)
then Let then
the
Theand
The (a)(c) (a) A of
If If
1. 2. 3. 4. 5. 6.
,
Single Calculus5.2
(b)11. (a)6. 13. 12.
(c)1.
Correct f)=x= For (c)Y= V2(y= r+i
ax) Equation
the
functions andMultiple
Ansver
(c)7.(d) 2.
e)=ysinr² |2r+rsin -V2r+ =
y a
of
line
Type defined which
Correct
is
;=0 ;0
(c)8.(b)3.
;0
parametrically is
=0 -/2xy=
() V2r+(y= Answers
b) tangent
and
(d) 9. (a)4.
to
both Type
by
the 2 the
10. (b) 5.
equations curves
(b) AnswersKey
y
=
ea Multiple
12. 15. 14.
(b, f"(2)=12f)=0
(c) (a) (0, The (d) (c) (b) (a) For (d) (c) (b) (a)
Genga ing Correct
c)
13.
Answers
(a,
b)
14. Type x-axis
curve
0) portion axes
but axes
touches equal
it y is is
btcx 4a.
ar
= of
portionnormalnormal normal
equal of is is xdoes does
normal normal
+ to to
2a.
inclinedinclined =
the tangent equation
curve
equation
2asin not normal
containedcontained at at t+exist exist at at
of of
not tangent
(a, an an
at
f(2)(d=2
)f"(1)(b=2
) at is a at t=0is
c) (1, angle sin t t=0isX-
t
inclined angle+twith = =
15. 0), betweenbetween coS" t 0 0
t 2x+y=0
(a,
then with 2
at I; 2y
x-axis, y =
b, 45° the the =
d) 0
co-ordinate
to co-ordinate -a
x-axis cos
x-axis
