PRACTICE (Click Here To Begin) ...the password is Practice
Name: Joseph Block
There are 20 problems (for your benefit since score does not count). The answers will be shown after your first
attempt.
#1 Points possible: 5. Total attempts: 0
The graph below is the function f (x)
5
4
3
2
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5
-2
-3
-4
-5
Find
lim
f (x)
x→ −1
Find
−
lim
f (x)
x→ −1
Find
+
lim
f (x)
x→ −1
Find f (
− 1)
#2 Points possible: 5. Total attempts: 0
Estimate the limit numerically or state that the limit does not exist (DNE):
sin(10x)
lim
x→0
x
Give your answer to at least three decimal places
#3 Points possible: 5. Total attempts: 0
Find the limit:
√x − 5
lim
x → 25
x − 25
Give an exact answer or keep at least three decimal places.
#4 Points possible: 5. Total attempts: 0
Let s(t)
= 6t
3
− 27t
2
− 72t
be the equation of motion for a particle. Find a function for the velocity.
v(t) =
Where does the velocity equal zero? [Hint: factor out the GCF.]
t =
and t =
Find a function for the acceleration of the particle.
a(t) =
#5 Points possible: 5. Total attempts: 0
If f (x)
√x − 7
=
, nd:
√x + 7
f ' (x)
=
f ' (4)
=
#6 Points possible: 5. Total attempts: 0
If f (x)
3x
2
+ 3x + 3
=
,
, then:
√x
f ' (x)
=
f ' (5)
=
#7 Points possible: 5. Total attempts: 0
If f (x)
= cos x − 6 tan x
, then
syntax error
f ' (x) =
f ' (5) =
#8 Points possible: 5. Total attempts: 0
Find the equation of the tangent line to the curve y
= 4 sin x
The equation of this tangent line can be written in the form y
at the point (
= mx + b
m =
and b
=
#9 Points possible: 5. Total attempts: 0
If f (x)
= sin
5
x
, nd f ' (x)
syntax error
Find f ' (4)
π
6
, 2)
where
.
#10 Points possible: 5. Total attempts: 0
Let f (x)
2
= √5x + 4x + 6
syntax error
f ' (x) =
f ' (2) =
#11 Points possible: 5. Total attempts: 0
x
1
y = (3 + e ) 3
Find
dy
dx
dy
syntax error
=
dx
Type sin(x) for sin(x) , cos(x) for cos(x), and so on.
Use x^2 to square x, x^3 to cube x, and so on.
Use ( sin(x) )^2 to square sin(x).
Do NOT simplify your answer.
#12 Points possible: 5. Total attempts: 0
Find the derivative of the function g(x)
e
x
=
2 − x
syntax error
g' (x) =
#13 Points possible: 5. Total attempts: 0
Let
f (x) = 4 ln(2x)
syntax error
f ' (x) =
f ' (5) =
#14 Points possible: 5. Total attempts: 0
If f (x)
= 3 arctan(8x)
Find f ' (2).
, nd f ' (x).
#15 Points possible: 5. Total attempts: 0
Use implicit di erentiation to determine
dy
dx
given the equation x
6
+ y
2
=
− 2
.
dy
=
dx
#16 Points possible: 5. Total attempts: 0
Use implicit di erentiation to nd
dy
dx
given the equation sin(xy)
= y
3
.
dy
=
dx
#17 Points possible: 5. Total attempts: 0
At noon, ship A is 30 nautical miles due West of ship B. Ship A is sailing West at 17 knots and ship B is sailing
North at 22 knots. How fast (in knots) is the distance between the ships changing at 6 PM? (Note: 1 knot is a speed
of 1 nautical mile per hour.)
knots
#18 Points possible: 5. Total attempts: 0
Let y
= tan(3x + 4)
.
Find the di erential dy when x
= 2
and dx
= 0.2
Find the di erential dy when x
= 2
and dx
= 0.4
#19 Points possible: 5. Total attempts: 0
Consider the function f (x)
The absolute maximum value is
and this occurs at x =
The absolute minimum value is
and this occurs at x =
2
= 4 − 7x ,
− 5 ≤ x ≤ 1
.
#20 Points possible: 5. Total attempts: 0
4
3
2
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5
-2
-3
-4
The function graphed above is:
Increasing on the interval(s)
Decreasing on the interval(s)