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Mat1022.E1MidtmWin211.docNAME ___________________________ MAT 1022.E1 Midterm Exam SCORE ________
Winter 2021
INSTRUCTIONS: Complete and return ONLY the last one page answer sheet!
I. Use lim (2x+1) = 7 to identify:
x(3
1. f(x) 2. c 3. L
II. Use the graph of the function, f, to answer each question.
1.
(
)
=
-
-
®
x
f
x
lim
1
2.
(
)
=
+
-
®
x
f
x
lim
1
3.
(
)
=
-
®
x
f
x
lim
1
4.
(
)
=
-
1
f
5. Is f continuous at
x = -1?
6.
=
-
®
)
(
lim
2
x
f
x
7.
(
)
=
+
®
x
f
x
lim
2
8.
(
)
=
®
x
f
x
lim
2
9.
(
)
=
2
f
10. Is f continuous at
x = 2?
III. Find each limit, if it exists.
1.
=
®
3
lim
0
x
2.
=
÷
ø
ö
ç
è
æ
+
®
3
2
lim
0
x
x
3.
=
-
+
-
®
1
1
2
1
lim
x
x
x
IV. Determine
(
)
x
f
¢
for(
)
x
f
as given.1.
(
)
=
¢
-
+
-
=
)
(
4
3
2
2
3
x
f
x
x
x
x
f
2.
=
¢
-
=
)
(
3
2
)
(
3
5
x
f
x
x
x
f
3.
(
)
(
)
=
¢
=
x
f
x
x
f
4
6
V. Is
(
)
ï
þ
ï
ý
ü
ï
î
ï
í
ì
£
>
+
=
1
x
if
2
1
if
1
2
x
x
x
x
f
continuous at x = 1? Why or Why not?VI. Write the equation of the tangent line to y=x^2 + 2x - 1 at (0,-1).
VII. At what point does the tangent line to y=3x^2-12x+5 have slope of zero?
VIII. The consumer price index (CPI) of an economy is described by the function
(
)
0
where
200
3
2
.
0
2
=
+
+
-
=
t
t
t
t
I
corresponds to the year 2015 for5
0
£
£
t
.1. What was the index value in 2015?
2. What was the average rate of change from 2015 to 2018?
3. How will the index be changing in 2019?
IX. The total cost function is C(x) =(0.1)x^2 - 30x + 200.
1. What is the marginal cost function?
2. What is marginal cost at output one hundred?
X. If P(x) =
(
)
3
4
3
+
x
()3
4
3
x
gives daily profit in hundreds of dollars. 1. Find the instantaneous rate of change of profit function. 2. What is the marginal profit at output 340?XI. List three equivalent notions and three different notations for a derivative.
XII. Matching
_____ 1.Right limit a. Slope of a tanget line
_____ 2.Left limit b. If y=e^x then y'=e^x.
_____ 3 Actual limit c. Marginal revenue
_____ 4. Function d. If y=[g(x)]^n then y'=n[g(x)]^(n-1)g'(x)
_____ 5. Continuous e. Slope of a secant line
_____ 6. Jump discontinuity f. If y = (uv) then y ‘ = uv’ + vu’
_____ 7. Removable discontinuity g. Approaching from the less than side
_____ 8. Average rate of change h. Function derived from another function
_____ 9. Derivative i. If y=ln x the y'=1/x
_____ 10. Derivative of a constant j. Hole in the graph
_____ 11. Product rule k. If y =(hi / lo) then y ‘ =(lo dhi – hi dlo)/(lo)^2
_____ 12. Power rule l. Zero
_____ 13. Quotient rule m. Approaching from the greater than side
_____ 14. Notions regarding derivatives n. Unique rule pairing domain to range
_____ 15. Notations for derivatives o. If y = x^n then y ‘ = nx^(n-1)
_____ 16. Chain rule p. Symbolic representations
_____ 17. Derivative of revenue q. Break in the graph
_____ 18. Instantaneous rate of change r. Left and right limits are the same
_____ 19. “ln” rule s. Actual limit equals functional value
_____ 20. “e” rule t. Ways of thinking about
Mat1022.E1 Midterm Exam Answer Sheet Winter 2021
I.Completion XII. Matching
I.1.________ 2.________ 3.________ 1._____ 10._____
11._____
II.1.______2.______3.______4.______5.______ 12._____
2._____ 13._____
6.______7.______8.______9.______10.______ 14._____
15._____
III.1.__________ 2.__________ 3.___________ 3._____ 16._____
17._____
lV.1.__________________ 2._______________ 3.____________ 4._____ 18._____
19._____
V.__________________________________________________ 5._____ 20._____
Vl._______________________________ 6._____
Vll.________________ 7._____
Vlll. 1._____________ 2._____________ 3._____________ 8._____
lX.1.____________________ 2.___________________
X. 1.____________________ 2.___________________
9._____
XI.Notions
1.____________________________________________
2.____________________________________________
3.____________________________________________
Notations
1._____________ 2._____________ 3._____________
