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)
