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MCV4U Final Exam Review # 2 (June 2018) Flashcards | StudBud
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MCV4U Final Exam Review # 2 (June 2018)
MCV4U Final Exam Review # 2 (June 2018)
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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
The vector (4,-1,0) exists in what plane ?
yz - plane
xy- plane
xyz-plane
xz-plane
2
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
3
Point B is a _________________?
global minimum
local maximum
global maximum
local minimum
4
Given the function f(x) = sin x
, the derivative f'(x) = ?
-cos x
-sin x
sin2x
cos x
5
Given the function f(x) = ln x
, the derivative f'(x) = ?
1/x
ex
x2
x-2
6
Given the function f(x) = x
4/5
, the derivative of the function f'(x) = ?
4x-1/5 / 5
4x-3/5 / 5
5x-1/5 / 4
5x-4/5 / 4
7
In the interval x ϵ [0,7], Point E and F are _________________?
global minimums
local minimums
global maximums
local maximums
8
Given the function f(x) = e
x
, the derivative f'(x) = ?
f'(x) = ex
1
1/x
0
9
If the displacement function is given as s(t) = t
4
, then the velocity function is ?
v(t) = 12t2
v(t) = 4t3 + t2
v(t) = 4t3
v(t) = 4t2
10
What is the Quotient Rule?
{(f ')(g) + (f)(g')} / g2
{(f )(g') - (f ')(g)} / g2
{(f ')(g) - (f)(g')} / g2
(f ')(g) + (f)(g')
11
What is the Product Rule ?
(f ')(g) - (g')(f)
none
(f )(g) + (g')(f')
(f ')(g) + (g')(f)
12
What is the derivative of the function f(x) = (2x
3
+ 1)
5
?
2x15 + 1
5(2x3 +1)4 (6x2)
5(2x3 +1)4
5(6x2 )4
13
The limit of the following function ?
5
0
7
undefined
14
Given the planes x + y - 2z + 4 = 0 and -2x -2y +4z + 8 = 0, these planes ?
skew
perpendicular
coincident
parallel
15
Determine the |(2,-1, 3)| (magnitude)
√8
√14
14
√12
16
Given the following symmetric equation, state the parametric equation for the y component?
y = 1+ 5t
y=1+ 4t
y = 3 + 6t
y = 2+5t
17
Given the function f(x) = e
-x
, the derivative f'(x) = ?
e-x
1
-e-x
xex
18
Given the function f(x) = 3
x
, the derivative f'(x) = ?
x . (3x-1)
x3
ln 3 . (3x)
3ex
19
The normal of the plane given the Cartesian Equation 2x -3y +7z = -4
(-2,3,-7)
4
(2,-3,7)
-4
20
log
3
x + 2log
3
y - log
3
z =
log3(xy2/z)
log3(x2y/z)
log3(xy/2z)
any of these
21
What is the direction vector of the vector equation r = (3,0,1) + t (-2,1,5)
(-2,1,5)
(5,1,-2)
(1,-1,-4)
(3,0,1)
22
Another notation to represent derivative is ?
y"
df
dx/dy
dy/dx
23
Given the function f(x) = cos x
, the derivative f'(x) = ?
-sin x
-cos x
cos x
sinx
24
Given A(2,2,1) and B(5,4,3), then vector AB is ?
AB = (3, 2, 2)
AB = (3, 2, 0)
AB = (-3, 2, -2)
AB = (3, 2, 1)
25
What type of asymptote is found when you find the limit f(x) as x-----> ±∞
horizontal asymptotes
slant asymptotes
oblique asymptotes
vertical asymptotes
26
Determining the values of x when f'(x) = 0 is finding the _______________ ?
local min/max. points
inflection points
asymptotes
roots
27
When two normals have a dot product equal to zero, the planes are ______?
skew
parallel
perpendicular
coincident
28
If the displacement function is given as s(t) = t
4
, then the acceleration function is ?
a(t) = 4t3 + t2
a(t) = 4t3
a(t) = 12t2
a(t) = 4t2
29
Determine the dot product of (2,0,3) and (1,4,0) ?
0
2
-2
4
30
Dot product is also referred to as _____, and the cross product is also referred to as ____.
square product, triangle product
scalar product, vector product
both of these
none of these
31
The process of finding a derivative by using limits and f(x+h)-f(x) is called ?
factoring
optimization
rationalizing
first principles
32
Given the function h(x) = -17 , the derivative of the function h'(x) = ?
-17x-1
-17
17
0
33
Given the following system, the two sets of intersecting lines are ?
parallel
coincident
perpendicular
skew
34
Point D is a _________________?
global maximum
local minimum
local maximum
global minimum
35
Given the function f(x) = ln(4x)
, the derivative f'(x) = ?
ln e
1/4
4x
1/x
36
Point A is a _________________?
local minimum
global maximum
global minimum
local maximum
37
The rate of change of a function is the _________________ ?
slope
reciprocal
absolute value
inverse
38
Given the following parametric equations, state the symmetric equation ?
(x+2)/1 = (y+1)/5 = (z-3)/6
(x-2)/-1 = (y+1)/5 = (z-3)/-6
(x-2)/1 = (y+1)/-5 = (z-3)/6
(x-2)/1 = (y-11)/-5 = (z+3)/6
39
The cross product of (1,1,0) and (1,0,1) is
(1, -1, -1)
(1,1,2)
(0,0,0)
(1,0,0)
40
The process of setting the derivative of a function equal to zero and solving it is called ?
tangent
optimization
dependence
first principles
41
Determining the values of x when f"(x) = 0 is finding the _______________ ?
inflection points
asymptotes
local min/max. points
y-intercept
42
Given the function f(x) = sin(4x)
, the derivative f'(x) = ?
4cos(4x)
cos(4x)
4cos x
-4sinx
43
Given the planes x + y - 2z + 4 = 0 and -2x -2y +4z -8 = 0, these planes ?
perpendicular
parallel
skew
coincident
44
Given the function f(x) = -3x
3
+ x
2
+ 1, the derivative of the function f'(x) = ?
-9x2 + 2x + 1
-9x2 + 2x
-9x2
-9x2 + 2
45
Given the function f(x) = 4x
5
, the derivative of the function f'(x) = ?
5x4
x2
20x4
80x3
46
What is the Chain Rule?
f'(g(x) . g'(x)
dy/du . du/dx
a way to determine the derivative of a composite function
all of these
47
Given the function g(x) = ∛x , the derivative of the function g'(x) = ?
x-1/3
x-2/3 / 3
2x-1/3 / 3
x2/3
48
The limit of the following function, as x ---> 3, is ______________
4
1
3
dne (does not exist)
49
The ______________ is when a tangent is used to find the rate of change (at only one point).
average rate of change
instantaneous rate of change
secant
y"
50
What is the value of ln e ?
cos x
none of these
0
e
