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