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A comprehensive review for calculus exam 02, covering key concepts such as differentiation, implicit differentiation, related rates, linear approximation, logarithmic differentiation, and parametric equations. It includes a variety of practice problems and solutions, designed to help students prepare for the exam. Well-organized and provides clear explanations of each concept, making it a valuable resource for students studying calculus.
Typology: Exercises
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10350 Exam 02 Review Name
Section
1a. Find
dy
dx
if sec(y) + e
xy = y +
p
2
⇡
4
⇡/ 4 .
1b. Find the equation of the tangent line to the curve sec(y) + e
xy = y +
p
2
⇡
4
⇡/ 4 at the point
⇣
1 ,
⇡
4
⌘
.
gBEI his (^) AM
Review
Implicit
y gix
LHS secly
mass secretes
p s
sexy
yth
teth RHS
to
instant a
mail.it (^) si
_belly
sexy
y
4
fly
III
y
t
1
t
and (^142)
1
tofu
Linan
x
at a point 20 meters from the base of the structure. A monkey climbs along the rope casting a shadow
on the ground directly below it. Find how fast the monkey is climbing along the rope when its shadow
is 6 meters from O if its shadowing is moving at a rate of 1/4 meter/sec towards the base of a the 10
meter structure. Assume there is no slack in the rope and the structure is perpendicular to the ground.
O (^) S
M
1
2
cm/min. If the initial length
of the radius is 4 cm, find how fast the volume of the cone is growing at time t = 3 minutes.
2
let
distance
dog
distance
(^20 6) dat ly
We want
similins's
1
E
In
So e'It Ex
ti l^
Ex'a
I't
F
g
9
V
2h's
V
t Gar thrift
V (^31 )
bar (^3) 3tr
I
2
2
33
min
2 x
2 y + 3y
3 = x
4 6.
Find how fast the particle is moving vertically at the point (1, 1) when its horizontal velocity at (1, 1)
is 4 units/sec. Is the particle heading upward or downward at the location (1, 1)?
x = 1 + ln(t
3 ); y =
2 e
t
Find also the cartesian equation of the curve given by the parametric equations.
correl Sitt^
x
a in D
2x2yt3y
3 1
y
96124
am
or to
so
upwards
tenyler
parametric version
e
e
xcel It In^
x
x
10350 Exam 02 Review Name
Section
end on the ground is moving away from the base of the wall at 0.5 ft/min.
(a) How fast is the angle changing when the end on the ground is 5
p
2 ft from the wall?
!
(b) How fast is the end on the wall moving when the end on the ground is 5
p
2 ft from the wall?
let
distance (^) of
off
equation
af
GHI E'HI^
to to
Costeltal Eiltal
1
mar
Hm
a
Éo E
Eh
y
same as
equation
Zyhly
we get
y
part
a
y
