Radhika Gupta
Math 2210-005, Fall 2014
October 1
Midterm 1
NAME:
INSTRUCTIONS:
1. Calculators are NOT allowed.
2. REMEMBER : Don’t spend too much time on problems which are worth very few points.
3. Don’t get stuck on a problem, KEEP MOVING ON arid in the end come back to the problems you
could not figure out on first try.
4. Show proper work to get full points. If your answer is wrong you still have a chance of getting
partial credit for the work.
5. TRUE/FALSE : Remember if a statement is false you can give an example riot satisfying the
statement as a proof but if the statement is true air example is riot sufficient.
Maximum Points = 50 points
Number of Pages : 7
Question No.
1
2
3
4
5
6
Total
Marks
BEST OF LUCK!!
1
Math 2210-005, Fall 2014
Radhika Gupta
October 1
1. [10 points] State True/False. Justify your answer to get full points
is a scalar multiple of
(a) If
x f = 0.
theii
,&C70
1-
e
(b) If(t).0(t) is a constant, then f(t).((t))’
‘-
0.
tUtf)
I
.
(c) The graph of the equation
ttie.
-tfh
sb i
t
=
0
•O
0 is the z-axis.
( is
LL
a spherical coordinate)
-
ox&
(d) Let=2+33 and f=i. Then Proj7=i.
11
P
G9Drn
R
£S
O41
_
2
P(e) The planes x + y + z
1 and 2x + 2y + 2z
=
1 intersect in a line.
LPA.
fri
P
‘[Ctn
.
(
+j + IC’)
imc, ‘lech,i
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Math 2210-005, Fall 2014
Radhika Gupta
October 1
4. [10 points]
(a) Graph the surface
1
IoLin
c
7
—
2 +
2y
322
= 1.
ki’LiQ-
tYt;Q
ki
(b) Draw level
o
2
2
7-
sets for the function
n-)V
z
+Y
ex
+
f(r. y, z) = 2
for
f(x, y, z)
—1,0, 1.2.
-1
2-
Le
(E,:
vaWe4
O
9 ki-)
hi/t
°‘
4—
I
iç
0,01
o)
V
.7-
1
i tt
O?vl
iO
7
Radhika Gupta
Math 2210-005, Fall 2014
October 1
5. [5 points] Find the slope of the tangent line to the curve of intersection of the surface z
the plane p = 3 at the point (1,3,3).
-nc
=
2
C,23)
6. [5 points] Show that the following limit does
not exist.
2
sin(x
liiii
(x,y)—*(O,O)
2
X
)
2
+ 2y
2
+y
[Hint : Choose two different lines through the origin along which limits are different.1
J2
3)—(OO)
CkIA2(nO
(‘zo)
0
rLi
eoc u
(jD)
e deL
L.
6
=
y and
2
x
Radhika Gupta
Math 2210-005, Fall 2014
October 1
Formula Sheet
1. Length of a parametrized curve (t)
=
f(t)i +
+ h(t)k from t
b is given by
=
a to t
=
D is given by
=
b
+ (g’(t))
2 + (h’(t))
dt
2
2, Distance d between a point
(Xo,
) and a plane Ax + By + Cz
0
yn, z
d—
—
9
+
Ax
+
0
D:
By
Cz
VA
+
2
B
C
3. Volume of parallelopiped spanned by the vectors d. b,
(dx b).L9
is given
by