review for final semester 2 calculus larson. 1.e11. b21. b31. b 2. e12. c22. a32. a 3. c13. e23....
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1.E 2. E 3. C 4. C 5. E 6. B 7. A 8. E 9. D 10. C 11. B 12. C 13. E 14. D 15. D 16. E 17. B 18. CTRANSCRIPT
Review for Final Semester 2
Calculus Larson
1. E 11. B 21. B 31. B2. E 12. C 22. A 32. A3. C 13. E 23. B 33. D4. C 14. D 24. A 34. B5. E 15. D 25. D 35. A6. B 16. E 26. C 36. A7. A 17. B 27. C 37. E8. E 18. C 28. B 38. B9. D 19. C 29. A10. C 20. C 30. C
1.E2. E3. C4. C5. E6. B7. A8. E9. D10. C
11. B12. C13. E14. D15. D16. E17. B18. C
1. E
2
2
sin 2
2cos 2 2 sin 2
2 cos 2 sin 2
y x xdy x x x xdxdy x x x xdx
2. E
42
32
32
2 1
4 2 1 4
16 2 1
y x
dy x xdxdy x xdx
3. C
2
2
33 2 22
12
112
1 2 1 12 3 3
u xdu xdx
x x dx udu
u c x c
4. C
3
2
4 5 3
' 12 5
' 1 7
1 4 so point 1,4
4 7 17 11
f x x x
f x x
f slope
f
y xy x
5. E set v(t) = 0
7. A inverse trig formula
2 2
2
1 arcsin
1 arcsin24
udu caa u
xdx cx
3 2
2
2
2 21 72 53
6 42 72 0
6 7 12 0
3 4 0
3, 4
x t t t t
v t t t
t t
t t
t t
6. B implicit differentiation
2 2
3,2
3 2 6 2
6 4 2 2
2 6 4 2
4 2 22 6 3
49
y x xydy dyy x x ydx dx
dyx y x ydx
dy x y x ydx x y x ydydx
8. E
23
13 2
1
2 1 3
y x
dy x xdx
10. C ¼ If Degree num= degree dem.
Then divide leading coef.
1 14 4
00
4
1 14 4
1 14
44
x u xe dx e du e
e
u xdu dx
9. D
11. B ½
If Degree num= degree dem.
Then divide leading coef.
12. C
12
12
4sin 21' 4sin 2 4cos21 1' 0 4 22 2
f x x
f x x x
f
3 12
20
311 2 22
02
1 12 216
1 2 16 5 4 12
162
x dudx u duux
u x
u xdu xdx
13. E
17. B average value
9 9 12
0 093
2
0
1
1 33
9 0 9
3 2 2 39 3
b
a
f x dxb a
xdx x dx
x
19. C find y’’<03 2
2
6
' 3 12'' 6 12 0
2
y x x
y x xy xx
2
– +
x
y
3 2 3
3 3 2
2 2 2 13
1 11 1 5 5 132 2
x dx x dx x dx
or
26. C
24. A 3 3
33
3
27 03 3 3
9 03
273
kx k
k
kk
12 2 2
212 22
12 2
27. 1 1
1' 1 22
1
1 2' 022
x x
xx x
x
C f x e e
ef x e ee
f
29. A2
2
2
ln ln lnln
ln ln ln ln ln 2 ln1 ln 2
ln1
eee
e
dx du u xx x u
e e
u x
du dxx
30.
1 11 1 1
1 1 1
C x y xydx dy xdy ydxdy xdy ydx dxdy x dx ydy y ydx x x
2
2 2
2 22 2
0 02
3
0
31. 5, 1
5 1 4 2
5 1 4
1 1643 3
B y y x
x x x
x dx x dx
x x
1819123
91
331
3123.33
31
0
3
32
1
0
2
x
uduudxx
3
20
31 1 22 2
0
2
1 135.216
1 16 12
162
x dx duux
u du u x
u xdu xdx
1
2 2
3 3
3
237. 2 44
' 2 4 1 2 4
4'' 4 4 1 4 44
E y xx
y x x
y x xx
4
+ –Concave down when y’’ is negative… for x > 4
y’’
Final – things to know…
Derivative of 1) trig, 2) a^u and e^x, 3) ln, 4) inverse trig, 5) x^n (power rule) … all with chain rule, Product rule, quotient rule
Slope and Equation of tangent lineIncreasing / decreasing ConcavityPoint of inflection
Implicit differentiation
Relative max/min
Particle at rest
Definite and indefinite Integrals with 1) trig, 2) absolute value, 3) a^u and e^x, 4) 1/x , 5) inverse trig, 6) x^n (power rule) … all with u-substitution
Average value
area
Limit – L’Hospital’s Rule
Exponential grow/decay