Unit 3 Key Questions
Task 1: Knowledge and Understanding
1. Find the first derivative of each of the following functions. (10 marks: 2 marks each)
4
x
x
a. f ( x )=x 3 +e 7
f ' ( x )=4 x 33 x ( ln 3)+
Rates of Change and Limits
Task 1: Knowledge and Understanding questions
1. Determine the limit of the function
x 2+3 x10
(
)
f x=
x2
as x
approaches 2.
(
2
x +3 x10
lim
x2
x 2
)
( x 22 x ) + ( 5 x10
Rates of Change and Derivatives
Task 1: Knowledge and Understanding Questions
1. Evaluate the following limits algebraically.
2
4 x +1
a. lim
x 3
Plugvalue x=3
2
4 ( 3 ) +1
4 ( 9 ) +1
=37
2
b.
x + 2
Unit 1: Rates of Change and derivatives (Part A) Assessment
Knowledge and Understanding
2
x +3 x10
1. Determine the limit of the function
as x approaches 2.
x2
x = 2 so we need to sub x = 2 into the e
Calculus and Vectors Unit 1 Assessment Questions
2
x +3 x +10
(
)
1. f x = x2
( x+5 )( x2 )
(x 2)
f ( x )=
f ( x )=(x+5)
f ( x )=( 2 ) +5
f ( x )=7
The limit of the function is 7.
4 x27
lim
2. x 4 x3
Komal Patel
ILC no: -16295012
MCV4UC
Unit 1
Task 1: Knowledge and Understanding questions
2
x +3 x10
1. Determine the limit of the function f ( x )=
as x approaches 2.
x2
Solution:
x 2+3 x10
f ( x )=
Unit 7 Key Questions
Task 1: Application Questions
1. Determine the angle between each of the following pairs of vectors. (10 marks: 5 marks each)
a. u =(2,4) and v =(1,3)
u v =( 2 ) ( 1 )(4 ) (3)
u v
Task 1: Knowledge and Understanding questions
2
1.Determine the limit of the function
f(x )=
x +3 x10
x2
as x approaches 2
Solution: As x approaches 2, the value of the function,
22 +3(2)10 4 +610 0
f
Unit Two Mark: 89 /100 = 89%
Komal Patel
ILC no: -16295012
MCV4UC
Unit 1
Task 1: Knowledge and Understanding questions
1. 11/11 Evaluate the following limits algebraically
2
4 x + 1 (2 marks)
a. lim
x
UNIT 1
1.
lim f ( x ) =
x 2
x 2 +3 x10
x 2
( x+5)(x2)
x2
lim f ( x ) =
x 2
lim f ( x ) =x+5
x 2
2+5
7
2.
lim f ( x ) =
x4
4 x 27
x3
4 x 27
x3
lim f ( x ) =
x 4
( 4 4 27 ) ( 43 )
57
3.
lim f ( h
Unit 7 Assessment for Learning
Task 1: Knowledge and Understanding questions
1. Find the first derivative of each of the following functions.
a. f ( x )=x 4 3 x +e x 7
b. g ( x ) =5 ( sin x )2
c.
h (
Unit 4 Assessment for Learning
Task 1: Knowledge and Understanding questions
1. Find the first derivative of each of the following functions.
a. f ( x )=x 4 3 x +e x 7
b. g ( x ) =5 ( sin x )2
c.
h (
Unit 6 Assessment for Learning
Task 1: Knowledge and Understanding questions
1. Find the first derivative of each of the following functions.
a. f ( x )=x 4 3 x +e x 7
b. g ( x ) =5 ( sin x )2
c.
h (
Unit 3 Assessment for Learning
Task 1: Knowledge and Understanding questions
1. Find the first derivative of each of the following functions.
a. f ( x )=x 4 3 x +e x 7
b. g ( x ) =5 ( sin x )2
c.
h (
Komal Patel
ILC no: -16295012
MCV4UC
Unit 2
Task 1: Knowledge and understanding functions
1. Find the first derivative of each of the following functions. (10 marks: 2
marks each)
a) f ( x )=x 4 3 x +
Linear functions are polynomials with a degree of 1.
When the slope of a line is positive, we say the line is
increasing, which means it goes up from left to right.
When the slope of a line is nega
Assignment 2
Task 1
2
4 x +1
1) a. lim )
x 3
3
=4( 2 +1
36+1=37
2
x +2 x8
b . lim 2
x 2 x 7 x+10
When we substitute x=2 the denominator becomes 0, resulting in an indeterminate form.
Hence we will tr
Assessment 3
4
x
x
1. a) f ( x )=x 3 +e 7
Using sum and differences rule,
x
Also for exponential functions, that is if g ( x ) =a where a 1 ,
'
x
g ( x )=k a where k=lna
Hence,
'
3
x
x
f ( x )=4 x ln
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MCV4U-B Lesson 2
Using Equation Editor in Microsoft Word 2007, 2010, and 2013
Using Equation Edito
Assignment 6
a =(7,1,2)
1.
( 5,4,4 )
b=
cos=
We know that,
In 3-space, the dot product of
cos=
Hence,
u . v
|u |v|
u=( x1 , y 1 , z 1 )v =( x 2 , y 2 , z 2 ) is u v =x 1 x 2 + y 1 y 2 + z 1 z 2
( 7,1
Assignment 5
1. We will start by drawing a diagram of the two vectors, tail to tail, with an angle of 55
Using the parallelogram law of vector addition, completing the parallelogram and
drawing the di
Unit 2: Rates of change and derivatives (Part B)
Knowledge and Understanding questions
1. Evaluate the following limits algebraically:
lim 4 x 2 +1 (2 marks)
a)
x 3
x = 3 so we need to sub x = 3 into
Unit 3: Exploring Derivative (Part A)
Knowledge and Understanding Questions
1. Find the first derivative of each of the following functions: (10 marks: 2 marks
each)
a) f ( x)=x 4 3 x + e x 7
3
x
f '
Unit 5 Key Questions
Task 1: Knowledge and Understanding Questions
1. Find the magnitude and direction of the resultant of two vectors u and v,
where u=3, v=5, and the angle between the vectors, when
Unit 2 Key Questions
Task 1: Knowledge and Understanding Questions
1. Evaluate the following limits algebraically.
lim 4 x 2+1
a.
x 3
(2 marks)
lim 4(3)2 +1
x 3
lim 4(9)+1
x 3
lim
x 3 =36 +1
lim
x 3