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Duplicate of MCV4U Final Exam Review
Duplicate of MCV4U Final Exam Review
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MCV4U Final Exam review #calculus #derivatives #vectors #limits #rateofchange
Flashcards
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Practice quiz
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Questions
36
Answers
1
The limit of the following function ?
undefined
5
0
7
2
What is the value of ln e ?
cos x
0
none of these
e
3
Point D is a _________________?
global minimum
global maximum
local maximum
local minimum
4
Given the function f(x) = 3
x
, the derivative f'(x) = ?
x3
x . (3x-1)
ln 3 . (3x)
3ex
5
Given the function g(x) = ∛x , the derivative of the function g'(x) = ?
x-2/3 / 3
x-1/3
2x-1/3 / 3
x2/3
6
Given the function h(x) = -17 , the derivative of the function h'(x) = ?
0
-17x-1
-17
17
7
Given the function f(x) = sin x
, the derivative f'(x) = ?
cos x
-sin x
-cos x
sin2x
8
If the displacement function is given as s(t) = t
4
, then the velocity function is ?
v(t) = 4t2
v(t) = 12t2
v(t) = 4t3
v(t) = 4t3 + t2
9
What is the Chain Rule?
dy/du . du/dx
a way to determine the derivative of a composite function
all of these
f'(g(x) . g'(x)
10
The ______________ is when a tangent is used to find the rate of change (at only one point).
instantaneous rate of change
average rate of change
secant
y"
11
Given the function f(x) = x
4/5
, the derivative of the function f'(x) = ?
5x-4/5 / 4
4x-1/5 / 5
4x-3/5 / 5
5x-1/5 / 4
12
log
3
x + 2log
3
y - log
3
z =
log3(xy/2z)
log3(xy2/z)
any of these
log3(x2y/z)
13
Determining the values of x when f"(x) = 0 is finding the _______________ ?
asymptotes
inflection points
y-intercept
local min/max. points
14
What is the Product Rule ?
(f )(g) + (g')(f')
(f ')(g) - (g')(f)
(f ')(g) + (g')(f)
none
15
Given the function f(x) = cos x
, the derivative f'(x) = ?
-cos x
-sin x
cos x
sinx
16
Given the function f(x) = 4x
5
, the derivative of the function f'(x) = ?
80x3
20x4
5x4
x2
17
Given the function f(x) = e
-x
, the derivative f'(x) = ?
e-x
1
xex
-e-x
18
The limit of the following function, as x ---> 3, is ______________
1
dne (does not exist)
3
4
19
What type of asymptote is found when you find the limit f(x) as x-----> ±∞
slant asymptotes
horizontal asymptotes
vertical asymptotes
oblique asymptotes
20
Given the function f(x) = x
100
+ 100x
-2
, the derivative of the function f'(x) = ?
100x99 - 200x-3
100x99 + 200x-3
100x99 - 200x-1
100x99 +100
21
Determining the values of x when f'(x) = 0 is finding the _______________ ?
roots
inflection points
asymptotes
local min/max. points
22
What is the Quotient Rule?
{(f ')(g) + (f)(g')} / g2
(f ')(g) + (f)(g')
{(f ')(g) - (f)(g')} / g2
{(f )(g') - (f ')(g)} / g2
23
If the displacement function is given as s(t) = t
4
, then the acceleration function is ?
a(t) = 4t2
a(t) = 12t2
a(t) = 4t3
a(t) = 4t3 + t2
24
Another notation to represent derivative is ?
dx/dy
y"
df
dy/dx
25
The process of finding a derivative by using limits and f(x+h)-f(x) is called ?
first principles
optimization
factoring
rationalizing
26
The process of setting the derivative of a function equal to zero and solving it is called ?
optimization
dependence
first principles
tangent
27
Point B is a _________________?
global minimum
local minimum
local maximum
global maximum
28
In the interval x ϵ [0,7], Point E and F are _________________?
global maximums
global minimums
local maximums
local minimums
29
Given the function f(x) = ln x
, the derivative f'(x) = ?
x-2
1/x
x2
ex
30
Given the function f(x) = sin(4x)
, the derivative f'(x) = ?
-4sinx
4cos(4x)
4cos x
cos(4x)
31
Given the function f(x) = e
x
, the derivative f'(x) = ?
f'(x) = ex
1
0
1/x
32
Given the function f(x) = -3x
3
+ x
2
+ 1, the derivative of the function f'(x) = ?
-9x2 + 2x
-9x2 + 2x + 1
-9x2
-9x2 + 2
33
Given the function f(x) = ln(4x)
, the derivative f'(x) = ?
1/4
ln e
1/x
4x
34
Point A is a _________________?
global minimum
local minimum
global maximum
local maximum
35
The rate of change of a function is the _________________ ?
inverse
absolute value
reciprocal
slope
36
What is the derivative of the function f(x) = (2x
3
+ 1)
5
?
5(6x2 )4
5(2x3 +1)4 (6x2)
5(2x3 +1)4
2x15 + 1
