Final Practice: 1. Find the inverse function f 1 (x) of f (x) = 2. Use a linear approximation to estimate 3 x2 3x + 4
7.7.
3. Use the Limit Denition of the Derivative to nd the derivative of f (x) =
Practice Problems on Sections 11.6 and 11.7 - ANSWERS
1. a)
24
3
24
1 ; b) 18
9
59
66
2. -13
3. The maximum is
< ln 6 1 , 1 , 1 > .
662
(ln 6 1 )2 +
6
1
36
+
1
4
in the direction of
4. a) (2 ln 2 +
Practice Problems on Section 11.3 - ANSWERS
1. a)
f
x
= 2x sin y + y 2 sin x,
b)
f
x
=
2
, f
1+(2x+3y )2 y
c)
f
x
= 4x3 ln(6y x)
d)
f
x
= 3 tan2 (4xy 3 ) sec2 (4xy 3 ) 4y 3 ,
e) f =
x
2.
2f
y2
2f
x
Practice Problems on Sections 10.8, 10.9, 11.2
1. A boy throws a rock up at a 30o angle with the horizontal from a
120 m high cli with the speed of 20 m/s.
If the air resistance is negligent, and the
Practice Problems on Section 10.6
For each of the equations below:
a) Identify (name) the surface;
b) Indicate the axis along which the surface is extended (if any);
c) Sketch the surface.
1. x = 2z 2
Practice Problems on Sections 10.4, 10.5
1. Given 3 vectors =< 1, 5, 2 >, =< 2, 1, 1 >, and
a
b
=< 3, 3, 0 >
c
a) Find .
ab
b) Find two unit vectors perpendicular to both and .
a
b
c) Determine wheth
Practice Problems on Sections 10.2 and 10.3
1. Given vectors =< 1, 1, 4 > and =< 1, 2, 2 > .
a
b
a) Find 3 2 .
a
b
b) Find .
ab
c) Find the angle between and .
a
b
d) Find two unit vectors parallel to
1. (10 pts.) Find all values of the constant c that make the function f (x) continuous
on (, ).
c2 x2 3x 1, if x < 1
f (x) =
3c cos(x 1), if x 1
answer: Continuity at x = 1 must have lim f (x) = lim+
1. (10 pts.) Find all values of the constant c that make the function f (x) continuous
on (, ).
c2 x2 3x 1, if x < 1
f (x) =
3c cos(x 1), if x 1
2. (10 pts.) Find the linear approximation of the funct
Final Practice:
x2
1. Find the inverse function f 1 (x) of f (x) =
3x + 4
y2
Set x =
and multiply both sides by 3y + 4.
3y + 4
f 1 (x) =
4x + 2
3x 1
2. Use a linear approximation to estimate 3 7.7.
1
Practice Problems on Sections 12.1, 12.2
1. Evaluate the integral
ye2xy dA, where
R
R = cfw_(x, y )|0 x 2, 0 y 3
2. Evaluate the integral
xy dA, where D is the region bounded by the
D
curves y = x2 4x