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