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MCV4U Final Exam Review Flashcards | StudBud
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MCV4U Final Exam Review
MCV4U Final Exam Review
50 terms
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MCV4U Final Exam review #calculus #derivatives #vectors #limits #rateofchange
Flashcards
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Questions
50
Answers
1
Dot product is also referred to as _____, and the cross product is also referred to as ____.
square product, triangle product
both of these
scalar product, vector product
none of these
2
If the displacement function is given as s(t) = t
4
, then the velocity function is ?
v(t) = 12t2
v(t) = 4t2
v(t) = 4t3 + t2
v(t) = 4t3
3
The normal of the plane given the Cartesian Equation 2x -3y +7z = -4
(-2,3,-7)
4
(2,-3,7)
-4
4
Given the function f(x) = 4x
5
, the derivative of the function f'(x) = ?
x2
20x4
5x4
80x3
5
The process of setting the derivative of a function equal to zero and solving it is called ?
dependence
optimization
first principles
tangent
6
Given the function f(x) = ln(4x)
, the derivative f'(x) = ?
1/4
1/x
4x
ln e
7
Given the function f(x) = sin(4x)
, the derivative f'(x) = ?
4cos x
cos(4x)
-4sinx
4cos(4x)
8
Given the function g(x) = ∛x , the derivative of the function g'(x) = ?
x2/3
x-1/3
x-2/3 / 3
2x-1/3 / 3
9
Point A is a _________________?
local maximum
local minimum
global maximum
global minimum
10
Given the function f(x) = 3
x
, the derivative f'(x) = ?
x . (3x-1)
x3
ln 3 . (3x)
3ex
11
Given the function f(x) = -3x
3
+ x
2
+ 1, the derivative of the function f'(x) = ?
-9x2 + 2
-9x2 + 2x + 1
-9x2 + 2x
-9x2
12
Given the following symmetric equation, state the parametric equation for the y component?
y = 2+5t
y=1+ 4t
y = 1+ 5t
y = 3 + 6t
13
Another notation to represent derivative is ?
dy/dx
dx/dy
df
y"
14
Given the planes x + y - 2z + 4 = 0 and -2x -2y +4z + 8 = 0, these planes ?
coincident
skew
parallel
perpendicular
15
What is the derivative of the function f(x) = (2x
3
+ 1)
5
?
2x15 + 1
5(2x3 +1)4
5(2x3 +1)4 (6x2)
5(6x2 )4
16
What is the value of ln e ?
e
none of these
cos x
0
17
The ______________ is when a tangent is used to find the rate of change (at only one point).
secant
instantaneous rate of change
average rate of change
y"
18
What type of asymptote is found when you find the limit f(x) as x-----> ±∞
slant asymptotes
oblique asymptotes
horizontal asymptotes
vertical asymptotes
19
The vector (4,-1,0) exists in what plane ?
xyz-plane
xy- plane
xz-plane
yz - plane
20
In the interval x ϵ [0,7], Point E and F are _________________?
local maximums
local minimums
global minimums
global maximums
21
Given the function f(x) = sin x
, the derivative f'(x) = ?
-sin x
cos x
sin2x
-cos x
22
What is the Product Rule ?
(f ')(g) + (g')(f)
(f )(g) + (g')(f')
(f ')(g) - (g')(f)
none
23
Given the function f(x) = x
100
+ 100x
-2
, the derivative of the function f'(x) = ?
100x99 - 200x-1
100x99 +100
100x99 + 200x-3
100x99 - 200x-3
24
Given the function f(x) = e
-x
, the derivative f'(x) = ?
xex
-e-x
1
e-x
25
Given the function h(x) = -17 , the derivative of the function h'(x) = ?
-17
17
0
-17x-1
26
Given the following system, the two sets of intersecting lines are ?
skew
parallel
perpendicular
coincident
27
Determining the values of x when f'(x) = 0 is finding the _______________ ?
roots
asymptotes
inflection points
local min/max. points
28
Given the function f(x) = x
4/5
, the derivative of the function f'(x) = ?
5x-4/5 / 4
5x-1/5 / 4
4x-1/5 / 5
4x-3/5 / 5
29
Given the function f(x) = cos x
, the derivative f'(x) = ?
sinx
-sin x
cos x
-cos x
30
The cross product of (1,1,0) and (1,0,1) is
(1, -1, -1)
(0,0,0)
(1,1,2)
(1,0,0)
31
Point D is a _________________?
global maximum
global minimum
local maximum
local minimum
32
Determine the dot product of (2,0,3) and (1,4,0) ?
4
2
0
-2
33
The rate of change of a function is the _________________ ?
inverse
slope
reciprocal
absolute value
34
Determining the values of x when f"(x) = 0 is finding the _______________ ?
local min/max. points
asymptotes
y-intercept
inflection points
35
Given the planes x + y - 2z + 4 = 0 and -2x -2y +4z -8 = 0, these planes ?
skew
perpendicular
coincident
parallel
36
What is the Chain Rule?
all of these
f'(g(x) . g'(x)
a way to determine the derivative of a composite function
dy/du . du/dx
37
Determine the |(2,-1, 3)| (magnitude)
√12
14
√14
√8
38
log
3
x + 2log
3
y - log
3
z =
log3(x2y/z)
log3(xy2/z)
log3(xy/2z)
any of these
39
If the displacement function is given as s(t) = t
4
, then the acceleration function is ?
a(t) = 4t2
a(t) = 4t3
a(t) = 12t2
a(t) = 4t3 + t2
40
Given the function f(x) = e
x
, the derivative f'(x) = ?
1
1/x
f'(x) = ex
0
41
The process of finding a derivative by using limits and f(x+h)-f(x) is called ?
factoring
optimization
rationalizing
first principles
42
Given the following parametric equations, state the symmetric equation ?
(x+2)/1 = (y+1)/5 = (z-3)/6
(x-2)/1 = (y-11)/-5 = (z+3)/6
(x-2)/-1 = (y+1)/5 = (z-3)/-6
(x-2)/1 = (y+1)/-5 = (z-3)/6
43
The limit of the following function, as x ---> 3, is ______________
4
3
dne (does not exist)
1
44
What is the Quotient Rule?
{(f )(g') - (f ')(g)} / g2
(f ')(g) + (f)(g')
{(f ')(g) - (f)(g')} / g2
{(f ')(g) + (f)(g')} / g2
45
Given A(2,2,1) and B(5,4,3), then vector AB is ?
AB = (3, 2, 1)
AB = (3, 2, 2)
AB = (-3, 2, -2)
AB = (3, 2, 0)
46
What is the direction vector of the vector equation r = (3,0,1) + t (-2,1,5)
(1,-1,-4)
(-2,1,5)
(5,1,-2)
(3,0,1)
47
When two normals have a dot product equal to zero, the planes are ______?
parallel
perpendicular
coincident
skew
48
The limit of the following function ?
undefined
0
5
7
49
Given the function f(x) = ln x
, the derivative f'(x) = ?
1/x
x-2
x2
ex
50
Point B is a _________________?
global maximum
global minimum
local maximum
local minimum
