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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.
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Correct 3.33 points out of 3. Flag question
one half the area of the circle with the same radius. Select one: a.
b.
c.
d.
e. None of the above
Correct 3.33 points out of 3. Flag question
this formula to find the volume of the given cone.
Select one: a.
b.
c.
d.
e. None of the above
Correct 3.33 points out of 3. Flag question
3.33 points out of 3. Flag question
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
Correct 3.33 points out of 3. Flag question
Evaluate the following as true or false.
Select one: a. true b. false
Correct 3.33 points out of 3. Flag question
Select one: a.
b.
c. The limit does not exist. d.
Incorrect 0.00 points out of 3. Flag question
Correct 3.33 points out of 3. Flag question
Select one: a.
b.
c.
d. The limit does not exist.
Correct 3.33 points out of 3. Flag question
Select one: a.
b.
c.
d.
Correct 3.33 points out of 3.
Flag question
Select one: a.
b.
c.
d.
Correct 3.33 points out of 3. Flag question
Select one: a.
b. − 6 c. (6) d. (- 3 )
Correct 3.33 points out of 3. Flag question
a. (0) b. (1) c. (x^6) d. (6x)
Correct 3.33 points out of 3. Flag question
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)
Correct 3.33 points out of 3. Flag question
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}} )
Correct 3.33 points out of 3. Flag question
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)
Correct 3.33 points out of 3. Flag question
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
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})
Correct 3.33 points out of 3. Flag question
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) )
Correct 3.33 points out of 3.
Flag question
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)
Correct 3.33 points out of 3. Flag question
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})
Correct 3.33 points out of 3. Flag question
(3x^2) d. (-x^3)
Correct 3.33 points out of 3. Flag question
What is the derivative of the function ( f (x) = 2x^2 + 3 ) at ( x )? Select one: a. (-4x) b. (4x) c. (2x) d. (-2x)