Calculus 1 Midterm 2
Calculus I Midterm 2
November 2013
2
1. (6 marks) Find the following limit:
lim (1 + sin 7 x )
cot 5 x
x →0 +
(
2. (3 marks) Find the derivative of y = 3 x + 5
2
)
sec x
Calculus I Midterm 2
November 2013
3
3. (Total 8 marks) Answer each question in the space provided. Do NOT simplify your answer. x2 − x
3 dy of the function f ( x) = ln( x3 )
a) Find dx e
[
( )]
b) If f ( x) = arcsin x
c) Find
( (
d sin 2 dx d) If f ( x) =
1
4 x
3
4
+ π 2 , find f ′(x)
tanh (x )
+ (2 x )
))
1
−e
2
(2 marks)
(2 marks)
(2 marks)
− log 7 (8 x) , find f ′(x )
(2 marks)
Calculus I Midterm 2
November 2013
4
4. (2 marks each; total 10 marks) For each of the following questions, select the correct answers by clearly shading in the appropriate boxes. Each question is worth 2 marks, but there may be anywhere from 0 to 4 correct answers. You will lose marks for each incorrect choice (i.e. selecting something that’s wrong, or missing something that’s correct, up to a maximum of 2 marks deduction per question (i.e. no negative marks ☺)
a) L’Hospital’s rule can be applied to which of the following limits:
lim x →0
b) If
5 x − tan 5 x x3 lim x →1−
1
x
1
lim ln x − x − 1
1− x2
x →1
x + x3 + x5
2
+ x3
lim 1 + x x →∞
xy + y 2 = 7 , then the value of dy at (1,−2) is: (only select one answer) dx -2/3
2/5
2/3
Not defined
c) Based on the following graph, which of the following statements are true:
The above graph has an absolute max at B and F
The above graph has a local min at A, C and E
The above graph has 3 points of inflection
The above graph has 2 local max’s and 2 local min’s
d) In order to find a linear approximation to find an approximate value for use f ( x) = x
L( x ) =
2
3
1
2
x+
6
3
with a = 8
use f ( x ) = x
L( x ) =
1
3
3
8.05 :
November 2013
2
1. (6 marks) Find the following limit:
lim (1 + sin 7 x )
cot 5 x
x →0 +
(
2. (3 marks) Find the derivative of y = 3 x + 5
2
)
sec x
Calculus I Midterm 2
November 2013
3
3. (Total 8 marks) Answer each question in the space provided. Do NOT simplify your answer. x2 − x
3 dy of the function f ( x) = ln( x3 )
a) Find dx e
[
( )]
b) If f ( x) = arcsin x
c) Find
( (
d sin 2 dx d) If f ( x) =
1
4 x
3
4
+ π 2 , find f ′(x)
tanh (x )
+ (2 x )
))
1
−e
2
(2 marks)
(2 marks)
(2 marks)
− log 7 (8 x) , find f ′(x )
(2 marks)
Calculus I Midterm 2
November 2013
4
4. (2 marks each; total 10 marks) For each of the following questions, select the correct answers by clearly shading in the appropriate boxes. Each question is worth 2 marks, but there may be anywhere from 0 to 4 correct answers. You will lose marks for each incorrect choice (i.e. selecting something that’s wrong, or missing something that’s correct, up to a maximum of 2 marks deduction per question (i.e. no negative marks ☺)
a) L’Hospital’s rule can be applied to which of the following limits:
lim x →0
b) If
5 x − tan 5 x x3 lim x →1−
1
x
1
lim ln x − x − 1
1− x2
x →1
x + x3 + x5
2
+ x3
lim 1 + x x →∞
xy + y 2 = 7 , then the value of dy at (1,−2) is: (only select one answer) dx -2/3
2/5
2/3
Not defined
c) Based on the following graph, which of the following statements are true:
The above graph has an absolute max at B and F
The above graph has a local min at A, C and E
The above graph has 3 points of inflection
The above graph has 2 local max’s and 2 local min’s
d) In order to find a linear approximation to find an approximate value for use f ( x) = x
L( x ) =
2
3
1
2
x+
6
3
with a = 8
use f ( x ) = x
L( x ) =
1
3
3
8.05 :