MATH 184 Quiz #2
October 8
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes.
(a) Differentiate y = ex (x3 − 1).
(b) Differentiate C(q) =
1+q
with respect to q.
1 + q2
ui
z
Answer:
e
Q
Answer:
Short answer questions — you must show your work
tic
2. 4 marks Each part is worth 2 marks.
x2 − 1, x < 3
is continuous at x = 3.
b + x, x ≥ 3
Answer:
Pr
ac
(a) Determine the value of b for which f (x) =
(b) Find the equation of the tanget line to y =
1
at x = 1.
x2
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
√
tangent line to y = 2x + 3 at x = 3. Please put a box around your final answer.
104/184 Quiz #2
October 8
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes.
(a) Differentiate f (t) = t−3 + et with respect to t.
ui
z
Answer:
Q
(b) Let g(x) = x3 + 1. For what value(s) of x is the slope of the tangent line of g(x) equal to
12?
Answer:
e
Short answer questions — you must show your work
tic
2. 4 marks Each part is worth 2 marks.
1/x, x ∈ (0, 2]
is continuous at x = 2.
cx,
x>2
Answer:
Pr
ac
(a) Determine the value of c for which f (x) =
(b) Differentiate y =
xex
. You do not need to simplify the answer.
x−2
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 compute the derivative
of
1
f (x) =
2x + 1
at x = 3. Please put a box around your final answer.
104/184 Quiz #2
October 8
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
ui
z
1. 2 marks Each part is worth 1 mark. Please write your answers in the boxes.
1
(a) Find the equation of the tangent line to y = x3 at x = .
2
Answer:
(b) Differentiate C(q) = (q − 1)(eq + 1) with respect to q.
Q
Answer:
e
Short answer questions — you must show your work
tic
2. 4 marks Each part is worth 2 marks.
ex ,
x<2
is continuous at x = 2.
2
1 + ax , x ≥ 2
Answer:
Pr
ac
(a) Determine the value of a for which f (x) =
(b) Differentiate y =
ex + x
. You do not need to simplify the answer.
x3 + 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 = 5x − 1
Pr
ac
tic
e
Q
ui
z
at x = 2. Please put a box around your final answer.
104/184 Quiz #2
October 8
Grade:
First Name:
Last Name:
Student-No:
Section:
Very short answer questions
Q
(b) 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.
x3
(a) Differentiate y = x .
e
Answer:
e
Answer:
tic
Short answer questions — you must show your work
2. 4 marks Each part is worth 2 marks.
√
x<2
a x,
is continuous at x = 2.
(a) Determine the value of a for which f (x) =
2
1+x , x≥2
Pr
ac
Answer:
(b) Find the equation of the tangent line to y = x3 at x = 13 .
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
tangent line to
1
y=
2x + 3
at x = 2. Please put a box around your final answer.