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Calculus I Midterm A

1) The document is a 15 question multiple choice midterm exam for Calculus I that instructs students to mark their answers on an answer sheet on page 4. 2) It contains 15 multiple choice questions testing a variety of calculus concepts including limits, derivatives, critical points, concavity, and volume optimization. 3) Students are advised to mark their answers on an answer sheet on page 4 to ensure their responses are considered for grading.

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648 views3 pages

Calculus I Midterm A

1) The document is a 15 question multiple choice midterm exam for Calculus I that instructs students to mark their answers on an answer sheet on page 4. 2) It contains 15 multiple choice questions testing a variety of calculus concepts including limits, derivatives, critical points, concavity, and volume optimization. 3) Students are advised to mark their answers on an answer sheet on page 4 to ensure their responses are considered for grading.

Uploaded by

omeryozkan4
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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MATH1851 - Calculus I Midterm Exam

Please do not forget to mark your answers to the questions on the answer sheet on Page 4
of the exam paper. Otherwise, your answers will not be considered.

Group A

Name and Student ID:

Department:
 
1 4
1. Find the limit lim −
x→2 x − 2 x2 − 4
1 1 1
A. Doesn’t Exist B. 2 C. 8 D. ∞ E. 4

p p 
2. Find the limit lim x2 + 2x − x2 − 2x
x→−∞
A. Doesn’t Exist B. 2 C. −2 D. 1 E. −1

3. On which intervel does the function f (x) = x3 − 15x + 1 = 0 has a solution?


A. [−4, −3] B. [−2, 0] C. [1, 2] D. [2, 3] E. Has no root

4. Which of the following statements is true?


A. Derivative of an even differentiable function is even
B. Derivative of an odd differentiable function is even
C. f (x) = x sgnx is differentiable at x = 0
D. f (x) = |x| is differentiable at x = 0
E. All continuous functions are differentiable

5. If y = tan kx, find y ′′ .


A. k 2 y(1 − y 2 ) B. 2k 2 y(1 − y 2 ) C. k 2 (1 + y 2 ) D. 2k 2 y(1 + y 2 ) E. k 2 (1 − y 2 )
√
6. If y = x x , find y ′ .
        
1 1 √ 1 1 1 1
A. √ ln x + 1 B. x x √ ln x + 1 C. √ ln x + 1
2 x 2   2 x 2  x 2
√ 1 1 √ 1 1
D. x x √ ln x + 1 E. x x √ ln x − 1
x 2 x 2

 
2x πx
7. What is the slope of the curve tan−1 = 2 at the point (1, 2) ?
y y
π−2 π−1 2−π π−2 π+2
A. B. C. D. E.
π−1 π−2 π−1 π+1 π+1

8. A man 2 m tall walks toward a lamppost on level ground at a rate of 0.5 m/s. If the lamp is 5 m high
on the post, how fast is the length of the man’s shadow decreasing when he is 3 m from the post?
3 1 2 5 1
A. B. C. D. E.
5 6 3 6 3

2
9. Find limx→0 (cos 2x)1/x
A. 1 B. e−2 C. e2 D. −2 E. 2

10. Which one of the following is a critical point of the function f (x) = 2x − sin−1 x ?
√
1 1 3 3 3
A. − √ B. √ C. − D. E.
3 3 2 2 2

Page 2
11. Which one of the following is a singular point of the function f (x) = 2x − sin−1 x ?
1 1 1
A. 0 B. − √ C. D. √ E. 1
2 2 2

12. Which one of the following is a local minimum value of the function f (x) = (x2 − 4)2 ?
A. −16 B. −2 C. 0 D. 2 E. 16

x2
13. On which interval the graph of the function f (x) = is concave up?
x2 +1
A. only on [ √13 , ∞) B. only on (−∞, − √13 ] C. [− √13 , √13 ]
D. (−∞, − √13 ] ∪ [ √13 , ∞) E. only on [0, ∞)

x
14. Which one of the following line is an asymptote to the graph of the function f (x) = √ ?
x2 + 1
1
A. y = 1 B. y = x C. y = 2 D. x = 1 E. x = 0

15. A box is made from a rectangular sheet of cardboard 70 cm by 150 cm by cutting equal squares out of
the four corners and bending uğ the resulting four flaps to make the sides of the box. Note that the box
has no top. What is the largest possible volume of the box?
175 115
A. 27 B. 15 C. 3 D. 10 E. 3

Page 3

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