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Calculus I: Derivatives Graded Exam - Straighterline MAT250 Topic 3, Exams of Animal Anatomy and Physiology

A graded exam for calculus i, specifically focusing on the topic of derivatives. It includes a series of multiple-choice questions covering various aspects of derivatives, such as finding the derivative of a function, applying the definition of the derivative, and understanding the relationship between derivatives and instantaneous rates of change. The exam provides valuable practice for students studying calculus i and helps them assess their understanding of derivatives.

Typology: Exams

2024/2025

Available from 03/13/2025

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Straighterline calculus I MAT250 Topic 3: Derivatives Graded Exam:
Topics 1-3 Questions and Answers (2025)
MAT250_TW_V4
Topic 3: Derivatives
Started on
Wednesday, March 5, 2025, 1:33 PM
State
Finished
Completed on
Wednesday, March 5, 2025, 1:50 PM
Time taken
16 mins 39 secs
Points
96.67/100.00
Grade
96.67 out of 100.00
Question 1
Correct
3.33 points out of 3.33
Flag question
Question text
The given region is the combination of a semicircle with radius 66 cm and a square with side
length 1212 cm. Find the area of the given region using the formula for the area of a
circle, A=πr2A=πr2 where rr is the circle's radius, and the formula for the area of a
square, A=s2A=s2 where ss is the length of a side of the square. Remember, a semicircle's area is
one half the area of the circle with the same radius.
Select one:
a.
72+18πcm272+18πcm2
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Download Calculus I: Derivatives Graded Exam - Straighterline MAT250 Topic 3 and more Exams Animal Anatomy and Physiology in PDF only on Docsity!

Straighterline calculus I MAT250 Topic 3: Derivatives Graded Exam:

Topics 1- 3 Questions and Answers (2025)

  • MAT250_TW_V
  • Topic 3: Derivatives

Started on Wednesday, March 5, 2025, 1:33 PM

State Finished

Completed on Wednesday, March 5, 2025, 1:50 PM

Time taken 16 mins 39 secs

Points 96.67/100.

Grade 96.67 out of 100.

Question 1

Correct 3.33 points out of 3. Flag question

Question text

The given region is the combination of a semicircle with radius 66 cm and a square with side

length 1212 cm. Find the area of the given region using the formula for the area of a

circle, A=πr 2 A=πr2 where rr is the circle's radius, and the formula for the area of a

square, A=s 2 A=s2 where ss is the length of a side of the square. Remember, a semicircle's area is

one half the area of the circle with the same radius. Select one: a.

72 + 18 πcm 2 72+18πcm

b.

144 + 18 πcm 2 144+18πcm

c.

72 + 6 πcm 2 72+6πcm

d.

144 + 6 πcm 2 144+6πcm

e. None of the above

Question 2

Correct 3.33 points out of 3. Flag question

Question text

The formula for the volume of a cone is V= 13 BhV=13Bh, where BB is the area of the base. Use

this formula to find the volume of the given cone.

Hint: The base of the cone is a circle and the formula for the area of a circle is A=πr 2 A=πr2,

where rr is the circle's radius.

Select one: a.

21 πft 3 21πft

b.

42 πft 3 42πft

c.

62 πft 3 62πft

d.

14 πft 3 14πft

e. None of the above

Question 3

Correct 3.33 points out of 3. Flag question

3.33 points out of 3. Flag question

Question text

A scientist is conducting an experiment. He starts with 1500 rabbits. After 60 days, the population of rabbits is 600. What is the average decrease in the number of rabbits per day? Select one: a. 15 rabbits per day b. 35 rabbits per day c. 25 rabbits per day d. 10 rabbits per day

Question 6

Correct 3.33 points out of 3. Flag question

Question text

Evaluate the following as true or false.

The notation limx→ 2 f(x)= 5 limx→2f(x)=5 states that the limit of the function ff at x= 5 x=5 is 22.

Select one: a. true b. false

Question 7

Correct 3.33 points out of 3. Flag question

Question text

What is the limit of the function in the graph at x= 4 x=4?

Select one: a.

b.

c. The limit does not exist. d.

Question 8

Incorrect 0.00 points out of 3. Flag question

Question text

For what value(s) of xx does the function given in the graph not have a limit?

Correct 3.33 points out of 3. Flag question

Question text

Determine, if it exists, limx→ 2 x 2 − 5 x+ 6 x 2 − 4 limx→2x2−5x+6x2−

Select one: a.

b.

c.

d. The limit does not exist.

Question 11

Correct 3.33 points out of 3. Flag question

Question text

The position of a car at time tt is given by the function p(t)=t 2 − 3 t− 6 p(t)=t2−3t− 6. At what time will

the velocity of the car be 77? Assume t≥ 0 t≥0.

Select one: a.

b.

c.

d.

Question 12

Correct 3.33 points out of 3.

Flag question

Question text

The position of a car at time tt is given by the function p(t)=t 2 + 2 t− 4 p(t)=t2+2t−4. What is the

velocity when p(t)= 11 p(t)=11? Assume t≥ 0 t≥0.

Select one: a.

b.

c.

d.

Question 13

Correct 3.33 points out of 3. Flag question

Question text

The position of a car at time tt is given by the function p(t)=t 2 + 2 t− 4 p(t)=t2+2t−4. What is the

velocity at t= 2 t=2? Assume t≥ 0 t≥0.

Select one: a.

b. − 6 c. (6) d. (- 3 )

Question 14

Correct 3.33 points out of 3. Flag question

a. (0) b. (1) c. (x^6) d. (6x)

Question 17

Correct 3.33 points out of 3. Flag question

Question text

What is the derivative of the function ( f (x) = 4x^3−2 ) at ( x=4 )? Select one: a. (192) b. (- 192 ) c. (- 188 ) d. (188)

Question 18

Correct 3.33 points out of 3. Flag question

Question text

Evaluate the derivative of the function: ( f (x) = (x − 2)^{−1} ) Select one: a. (0) b. (1)

c. ( \displaystyle\frac{1}{(x-2)^{2}} ) d. ( - \displaystyle\frac{1}{(x-2)^{2}} )

Question 19

Correct 3.33 points out of 3. Flag question

Question text

Find the slope of the line tangent to ( f(x) = x^2 - x ) at the point ( x=2 ). Select one: a. (0) b. (3) c. (2) d. (4)

Question 20

Correct 3.33 points out of 3. Flag question

Question text

What is the average rate of change of the function ( y = 4x^3 - 2 ) between ( x = 2 ) and ( x = 4 )? Select one: a. (112) b. (- 112 ) c. (110)

3.33 points out of 3. Flag question

Question text

The instantaneous rate of change of a ball (in (\hbox{ft/sec})) is given by ( f'(x) =\displaystyle\frac{1}{\sqrt{x}} ). When was the ball travelling at a rate of ( \displaystyle\frac{1}{4} , \hbox{ft/sec})? Select one: a. (2 , \hbox{ft/sec}) b. (\displaystyle\frac{1}{2} , \hbox{ft/sec}) c. (4 , \hbox{ft/sec}) d. (16 , \hbox{ft/sec})

Question 24

Correct 3.33 points out of 3. Flag question

Question text

What is the average rate of change of the function ( y = 4x^3 − 2 ) between ( x = x_1 ) and ( x = x_2 ) Select one: a. (4(x_2^2 + x_2x_1-x_1^2)) b. (4(x_2^2 - x_2x_1+x_1^2)) c. (4(x_2^2 - x_2x_1-x_1^2)) d. (4(x_2^2 + x_2x_1+x_1^2) )

Question 25

Correct 3.33 points out of 3.

Flag question

Question text

What is the slope of the tangent line of the function ( f(x)=−2x^2+3x−1 ) at ( x=−2 )? Select one: a. (- 9 ) b. (- 11 ) c. (9) d. (11)

Question 26

Correct 3.33 points out of 3. Flag question

Question text

Let ( f'(x) = 3x^2+4x ) define the instantaneous rate of change (in (\hbox{ft/min})) of a car moving along the (x)-axis. What is the instantaneous rate of change at time (1 , \hbox{min})? Select one: a. (10 , \hbox{ft/min}) b. (7 , \hbox{ft/min}) c. (3 , \hbox{ft/min}) d. (4 , \hbox{ft/min})

Question 27

Correct 3.33 points out of 3. Flag question

Question text

(3x^2) d. (-x^3)

Question 30

Correct 3.33 points out of 3. Flag question

Question text

What is the derivative of the function ( f (x) = 2x^2 + 3 ) at ( x )? Select one: a. (-4x) b. (4x) c. (2x) d. (-2x)