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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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Questions
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Answers
1
Determine the |(2,-1, 3)| (magnitude)
√14
√12
14
√8
2
Given the function f(x) = cos x
, the derivative f'(x) = ?
-cos x
cos x
sinx
-sin x
3
If the displacement function is given as s(t) = t
4
, then the acceleration function is ?
a(t) = 4t3
a(t) = 12t2
a(t) = 4t2
a(t) = 4t3 + t2
4
Given the function f(x) = ln x
, the derivative f'(x) = ?
x-2
ex
1/x
x2
5
The rate of change of a function is the _________________ ?
reciprocal
inverse
slope
absolute value
6
Another notation to represent derivative is ?
y"
df
dx/dy
dy/dx
7
Determine the dot product of (2,0,3) and (1,4,0) ?
2
-2
4
0
8
When two normals have a dot product equal to zero, the planes are ______?
perpendicular
coincident
skew
parallel
9
Given the function g(x) = ∛x , the derivative of the function g'(x) = ?
x2/3
2x-1/3 / 3
x-2/3 / 3
x-1/3
10
The ______________ is when a tangent is used to find the rate of change (at only one point).
secant
instantaneous rate of change
y"
average rate of change
11
Given the function f(x) = x
4/5
, the derivative of the function f'(x) = ?
5x-1/5 / 4
5x-4/5 / 4
4x-3/5 / 5
4x-1/5 / 5
12
What is the direction vector of the vector equation r = (3,0,1) + t (-2,1,5)
(3,0,1)
(-2,1,5)
(5,1,-2)
(1,-1,-4)
13
Dot product is also referred to as _____, and the cross product is also referred to as ____.
none of these
scalar product, vector product
square product, triangle product
both of these
14
Given the function f(x) = x
100
+ 100x
-2
, the derivative of the function f'(x) = ?
100x99 + 200x-3
100x99 - 200x-3
100x99 +100
100x99 - 200x-1
15
Given the following symmetric equation, state the parametric equation for the y component?
y=1+ 4t
y = 2+5t
y = 3 + 6t
y = 1+ 5t
16
What is the Quotient Rule?
(f ')(g) + (f)(g')
{(f ')(g) - (f)(g')} / g2
{(f )(g') - (f ')(g)} / g2
{(f ')(g) + (f)(g')} / g2
17
The process of setting the derivative of a function equal to zero and solving it is called ?
first principles
optimization
tangent
dependence
18
Given the function f(x) = sin(4x)
, the derivative f'(x) = ?
4cos(4x)
-4sinx
4cos x
cos(4x)
19
Given the function h(x) = -17 , the derivative of the function h'(x) = ?
-17
17
0
-17x-1
20
Determining the values of x when f'(x) = 0 is finding the _______________ ?
inflection points
local min/max. points
roots
asymptotes
21
What is the Product Rule ?
(f ')(g) + (g')(f)
(f ')(g) - (g')(f)
none
(f )(g) + (g')(f')
22
Given the function f(x) = ln(4x)
, the derivative f'(x) = ?
1/x
1/4
4x
ln e
23
Given the function f(x) = sin x
, the derivative f'(x) = ?
cos x
-sin x
sin2x
-cos x
24
The vector (4,-1,0) exists in what plane ?
xz-plane
xyz-plane
yz - plane
xy- plane
25
The limit of the following function, as x ---> 3, is ______________
4
1
dne (does not exist)
3
26
Given the function f(x) = 3
x
, the derivative f'(x) = ?
x3
ln 3 . (3x)
x . (3x-1)
3ex
27
Given A(2,2,1) and B(5,4,3), then vector AB is ?
AB = (3, 2, 1)
AB = (3, 2, 0)
AB = (-3, 2, -2)
AB = (3, 2, 2)
28
log
3
x + 2log
3
y - log
3
z =
log3(xy/2z)
log3(x2y/z)
any of these
log3(xy2/z)
29
Given the function f(x) = e
-x
, the derivative f'(x) = ?
xex
-e-x
e-x
1
30
Determining the values of x when f"(x) = 0 is finding the _______________ ?
inflection points
asymptotes
y-intercept
local min/max. points
31
What is the value of ln e ?
0
e
none of these
cos x
32
The normal of the plane given the Cartesian Equation 2x -3y +7z = -4
(-2,3,-7)
(2,-3,7)
4
-4
33
The process of finding a derivative by using limits and f(x+h)-f(x) is called ?
optimization
first principles
rationalizing
factoring
34
What is the Chain Rule?
f'(g(x) . g'(x)
all of these
dy/du . du/dx
a way to determine the derivative of a composite function
35
Given the function f(x) = -3x
3
+ x
2
+ 1, the derivative of the function f'(x) = ?
-9x2 + 2
-9x2 + 2x
-9x2
-9x2 + 2x + 1
36
Given the function f(x) = e
x
, the derivative f'(x) = ?
0
1
f'(x) = ex
1/x
37
The limit of the following function ?
7
0
5
undefined
38
Point B is a _________________?
local minimum
local maximum
global minimum
global maximum
39
Given the function f(x) = 4x
5
, the derivative of the function f'(x) = ?
20x4
80x3
x2
5x4
40
Point A is a _________________?
local maximum
global maximum
global minimum
local minimum
41
What is the derivative of the function f(x) = (2x
3
+ 1)
5
?
5(2x3 +1)4
5(2x3 +1)4 (6x2)
2x15 + 1
5(6x2 )4
42
In the interval x ϵ [0,7], Point E and F are _________________?
global minimums
local maximums
local minimums
global maximums
43
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 + t2
v(t) = 4t3
44
Point D is a _________________?
global minimum
local minimum
local maximum
global maximum
45
What type of asymptote is found when you find the limit f(x) as x-----> ±∞
horizontal asymptotes
slant asymptotes
vertical asymptotes
oblique asymptotes
