104/184 Quiz 2
October 9
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
(a) Differentiate C(q) = q 3 eq with respect to q..
ui
z
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes. You do not
need to simplify the answer.
Answer:
x5
.
ex + 3
Q
(b) Differentiate y =
e
Answer:
tic
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
(
Answer:
Pr
ac
(a) Determine the value of a for which f (x) =
1 + eax , x < 4
is continuous at x = 4.
√
x,
x≥4
(b) Find the equation of the tangent line to y = 2x4 at x = −1.
Answer:
Long answer question — you must show your work
Pr
ac
tic
e
Q
ui
z
3. 4 marks Use the definition of the derivative, i.e.the limit process, to find the slope of the
tagent line to the graph of
2
y=
3x + 1
at x = 2. Please put a box around your final answer.
104/184 Quiz #2
October 9
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
Q
(b) Differentiate C(q) = q −2 eq with respect to q.
ui
z
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes. You do not
need to simplify the answer.
ex
(a) Differentiate y =
.
2x + 1
Answer:
e
Answer:
tic
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
ln(ax) + 2, x < 2
is continuous at x = 2.
3x − 4,
x≥2
Answer:
Pr
ac
(a) Determine the value of a for which f (x) =
(b) Find the equation of the tanget line to y = 3x2 + x at x = 2.
Answer:
Long answer question — you must show your work
3. 4 marks Use the definition of the derivative, i.e. the limit process, to find the slope of the
tangent line to
√
y = 2x + 3
Pr
ac
tic
e
Q
ui
z
at x = 3. Please put a box around your final answer.
104/184 Quiz #2
October 9
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
(a) Differentiate P (q) = (q + 1)eq with respect to q.
ui
z
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes. You do not
need to simplify the answer.
Answer:
1 + x2
.
1 + ex
Q
(b) Differentiate y =
e
Answer:
tic
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
1 + x + x2 , x < 1
is continuous at x = 1.
e−ax ,
x≥1
Answer:
Pr
ac
(a) Determine the value of a for which f (x) =
(b) Find the equation of the tangent line to y = x13 at x = −1.
Answer:
Long answer question — you must show your work
Pr
ac
tic
e
Q
ui
z
3. 4 marks Use the definition of the derivative, ie. the limit process, to find the slope of the
tangent line to
1
y=
2x − 3
at x = 2. Please put a box around your final answer.
104/184 Quiz #2
October 9
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
(a) Differentiate C(q) = q 3 eq with respect to q.
ui
z
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes. You do not
need to simplify the answer.
Answer:
x
.
ex + x2
Q
(b) Differentiate y =
e
Answer:
Short answer questions — you must show your work
tic
2. 4 marks Each part is worth 2 marks.
(a) Find the equation of the tanget line to y = x3 at x = −1.
Pr
ac
Answer:
√
x + 8, x < 1
(b) Determine the value of a for which f (x) =
is continuous at x = 1.
ax
e ,
x≥1
Answer:
Long answer question — you must show your work
3. 4 marks Use the definition of the derivative, i.e. the limit process, to find the slope of the
tangent line to
√
y = 4x + 1
Pr
ac
tic
e
Q
ui
z
at x = 2. Please put a box around your final answer.