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Study Guide for the 2nd Exam MTH241
Exam Date: 28th October 2011. In class
Exam Covers Sections 14
.
1

14
.
8
You must know the followings
1. Domain of the function.
2. Limit and Continuity
Prove or disprove the existance of limit. Do all the problems from the handout which I distributed
in class
3. Partial Derivatives. Find
f
x
,f
y
,f
xx
,f
yy
,f
xy
etc
4. Tangent plances and linearizations.
Equation of the tangent plane of the curve
z
=
f
(
x,y
) at (
a,b
) is given by
f
x
(
a,b
)(
x

a
) +
f
y
(
a,b
)(
y

b
)

(
z

f
(
a,b
)) = 0
Linearization of
f
(
x,y
) = 0 around (
a,b
) is given by
f
x
(
a,b
)(
x

a
) +
f
y
(
a,b
)(
y

b
)

(
z

f
(
a,b
)) = 0.
5. Chain Rule.
Must know
z
=
f
(
x,y
)
,x
=
g
(
t
)
,y
=
h
(
t
)
⇒
dz
dt
=
∂f
∂x
dx
dt
+
∂f
∂y
dy
dt
z
=
f
(
x,y
)
,x
=
g
(
s,t
)
,y
=
h
(
s,t
)
⇒
dz
ds
=
∂f
∂x
∂x
∂s
+
∂f
∂y
∂y
∂s
⇒
dz
dt
=
∂f
∂x
∂x
∂t
+
∂f
∂y
∂y
∂t
Implicit Diﬀerentiation:
F
(
x,y
) = 0
,y
=
f
(
x
)
⇒
dy
dx
=

F
x
F
y
6. Directional Derivatives, Gradiant, Maximum rate of change. Finding the equations of
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This document was uploaded on 11/04/2011 for the course MTH 240 at SUNY Buffalo.
 Fall '11
 Chakraborty
 Continuity

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