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z z z z z z z z
Exam
Name
MULTIPLEz CHOICE.z Choosez thez onez alternativez thatz bestz completesz thez statementz orz answersz thez question.
Findzthez averagez velocityz ofz anzobjectzwhichzfollowszthez positionzfunctionzs(t)z overz thez givenzinterval.
1) s(t)z=zt2z+z2t,z[2,z7] 1)z
z63 z55
A) 5 B) 7 C) 11 D)z 9
2) s(t)z=z6t3z-z8t2z+z2,z[-8,z-1] 2) z
A) 12 B)z510 C)z-
z
z D) -z3570
1
2
z
7
3) s(t)z= 2t,z[2,z8] 3) z
A) z 3z 1
z
7 B) - z z C)z 2 D)z
10 3
z 3z z
4) s(t)z=z ,z[4,z7] 4) z
tz-z2
A) z 3z B) 1
z
-z 2 C)z D)z 7
10 3
5) 7
z
s(t)z=z4t2,z 0,z 5) z
4
z 3z z1
A) -z B) 3 C) 2 D)z 7
10
6) s(t)z=z-3t2z-zt,z[5,z6] 6) z
z1 z1
A) 2 B) -34 C)z-z D) -2
6
7) π
s(t)z=zsinz(4t),z 0,z 7) z
8
8
z π z4 z8
A) -z B) C) π D) π
π 8
8) πz π
s(t)z=z5z+ztanzt,z -z ,z 8) z
4z z 4
z4 z4
A) -z 16
C) -z
z
B) π D) 0
π 11
1
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z z z z z z z z
Usez thez tablez tozfindzthez instantaneouszvelocityzofz yz atzthez specifiedzvaluez ofz x.
9) xz=z1. 9) z
xz z y
0 0
0.2z0.02
0.4z0.08
0.6z0.18
0.8z0.32
1.0z 0.5
1.2z0.72
1.4z0.98
A)z 0.5 B)z 1.5 C)z 2 D)z 1
10) xz=z1. 10) z
x y
0 0
0.2z0.01
0.4z0.04
0.6z0.09
0.8z0.16
1.0z0.25
1.2z0.36
1.4z0.49
A)z 1 B)z 0.5 C)z 1.5 D)z 2
11) xz=z1. 11) z
x y
0 0
0.2z0.12
0.4z0.48
0.6z1.08
0.8z1.92
1.0z z 3
1.2z4.32
1.4z5.88
A)z 6 B)z 8 C)z 4 D)z 2
2
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z z z z z z z z
12) xz=z2. 12) z
xz z y
0z 10
0.5z38
1.0z58
1.5z70
2.0z74
2.5z70
3.0z58
3.5z38
4.0z10
A)z -8 B)z0 C)z8 D)z4
13) xz=z1. 13) z
x y
0.900z -0.05263
0.990z -0.00503
0.999z -0.0005
1.000z 0.0000
1.001z 0.0005
1.010z 0.00498
1.100z 0.04762
A) 1 B)z0 C)z0.5 D)z -0.5
Findzthezslopezofz thezcurvezforzthezgivenzvaluez ofzx.
14) yz=zx2z+z5x,zxz=z4 14) z
A) z1 B) z 4z
slopezisz slopezisz-39 C)zslopezisz13 D)zslopezis -
z z
z 25
20
15) yz=zx2z+z11xz-z15,zxz=z1 15) z
A) z 1z
B) slopezisz-39 C)zslopezisz-
slopezisz z4 D)z slopezisz13
20 z
zz
2
5
16) yz=zx3z-z9x,zxz=z1 16) z
A) slopezisz1 B)z slopezisz-6 C)zslopezisz-3 D)zslopezisz3
17) yz=zx3z-z3x2z+z4,zxz=z3 17) z
A) slopezisz0 B)z slopezisz1 C)z slopez isz -9 D)z slopezisz9
18) yz=z-3z-zx3,zxz=z1 18) z
A) slopezisz0 B)zslopezisz3 C)zslopezisz-1 D)z slopezisz-3
3
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z z z z z z z z
Solvezthez problem.
19) Givenz z lim f(x)z=zLl,z z lim f(x)z=zLr,zandz Llz≠z Lr,zwhichzofzthezfollowingzstatementszisztrue? 19) z
x→0- x→0+
I. limz f(x)z=zLlz
x→0
II. limz f(x)z=zLrz
x→0
III. limz f(x)zdoesznotzexist.
zx→0
A) III B)z II C)z none D)z I
20) Givenz z lim f(x)z=zLl,z z lim f(x)z=z Lrz,zandzLlz=zLr,zwhichzofzthezfollowingzstatementsziszfalse? 20) z
x→0- x→0+
I. limz f(x)z=zLlz
x→0
II. limz f(x)z=zLrz
x→0
III. limz f(x)zdoesznotzexist.
zx→0
A) II B)z I C)z III D)z none
21) Ifz limz f(x)z=zL,zwhichzofzthezfollowingzexpressionszareztrue?z 21) z
x→0
I. limz f(x)zdoesznotzexist.
x→0-
II. limzx zf(x)zdoesznotzexist
→0+
III. limz .zf(x)z=zL
x→0-
f(x)z=zL
IV. limzx
→0+
A) IIzandzIIIzonly B)z IzandzIIzonly C)z IzandzIVzonly D)z IIIzandzIVzonly
22) Whatzconditions,zwhenzpresent,zarezsufficientztozconcludezthatzazfunctionzf(x)zhaszazlimitzaszxz 22) z
approacheszsomezvaluezofza?
A) Eitherzthezlimitzofzf(x)z aszx→az fromzthezleftzexistszorzthez limitzofzf(x)z aszx→az fromzthezrightzexists
B) f(a)zexists,zthezlimitzofzf(x)zaszx→azfromzthezleftzexists,zandzthezlimitzofzf(x)zaszx→azfromzthezrightz
exists.
C) Thezlimitzofzf(x)zaszx→azfromzthezleftzexists,zthezlimitzofzf(x)zaszx→azfromzthezrightzexists,zandzatzl
eastzonezofzthesezlimitsziszthezsamezaszf(a).
D) Thezlimitzofzf(x)zaszx→azfromzthezleftzexists,zthezlimitzofzf(x)zaszx→azfromzthezrightzexists,zandzt
heseztwozlimitszarezthezsame.
4
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z z z z z z z z
Exam
Name
MULTIPLEz CHOICE.z Choosez thez onez alternativez thatz bestz completesz thez statementz orz answersz thez question.
Findzthez averagez velocityz ofz anzobjectzwhichzfollowszthez positionzfunctionzs(t)z overz thez givenzinterval.
1) s(t)z=zt2z+z2t,z[2,z7] 1)z
z63 z55
A) 5 B) 7 C) 11 D)z 9
2) s(t)z=z6t3z-z8t2z+z2,z[-8,z-1] 2) z
A) 12 B)z510 C)z-
z
z D) -z3570
1
2
z
7
3) s(t)z= 2t,z[2,z8] 3) z
A) z 3z 1
z
7 B) - z z C)z 2 D)z
10 3
z 3z z
4) s(t)z=z ,z[4,z7] 4) z
tz-z2
A) z 3z B) 1
z
-z 2 C)z D)z 7
10 3
5) 7
z
s(t)z=z4t2,z 0,z 5) z
4
z 3z z1
A) -z B) 3 C) 2 D)z 7
10
6) s(t)z=z-3t2z-zt,z[5,z6] 6) z
z1 z1
A) 2 B) -34 C)z-z D) -2
6
7) π
s(t)z=zsinz(4t),z 0,z 7) z
8
8
z π z4 z8
A) -z B) C) π D) π
π 8
8) πz π
s(t)z=z5z+ztanzt,z -z ,z 8) z
4z z 4
z4 z4
A) -z 16
C) -z
z
B) π D) 0
π 11
1
mynursytest.store
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z z z z z z z z
Usez thez tablez tozfindzthez instantaneouszvelocityzofz yz atzthez specifiedzvaluez ofz x.
9) xz=z1. 9) z
xz z y
0 0
0.2z0.02
0.4z0.08
0.6z0.18
0.8z0.32
1.0z 0.5
1.2z0.72
1.4z0.98
A)z 0.5 B)z 1.5 C)z 2 D)z 1
10) xz=z1. 10) z
x y
0 0
0.2z0.01
0.4z0.04
0.6z0.09
0.8z0.16
1.0z0.25
1.2z0.36
1.4z0.49
A)z 1 B)z 0.5 C)z 1.5 D)z 2
11) xz=z1. 11) z
x y
0 0
0.2z0.12
0.4z0.48
0.6z1.08
0.8z1.92
1.0z z 3
1.2z4.32
1.4z5.88
A)z 6 B)z 8 C)z 4 D)z 2
2
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z z z z z z z z
12) xz=z2. 12) z
xz z y
0z 10
0.5z38
1.0z58
1.5z70
2.0z74
2.5z70
3.0z58
3.5z38
4.0z10
A)z -8 B)z0 C)z8 D)z4
13) xz=z1. 13) z
x y
0.900z -0.05263
0.990z -0.00503
0.999z -0.0005
1.000z 0.0000
1.001z 0.0005
1.010z 0.00498
1.100z 0.04762
A) 1 B)z0 C)z0.5 D)z -0.5
Findzthezslopezofz thezcurvezforzthezgivenzvaluez ofzx.
14) yz=zx2z+z5x,zxz=z4 14) z
A) z1 B) z 4z
slopezisz slopezisz-39 C)zslopezisz13 D)zslopezis -
z z
z 25
20
15) yz=zx2z+z11xz-z15,zxz=z1 15) z
A) z 1z
B) slopezisz-39 C)zslopezisz-
slopezisz z4 D)z slopezisz13
20 z
zz
2
5
16) yz=zx3z-z9x,zxz=z1 16) z
A) slopezisz1 B)z slopezisz-6 C)zslopezisz-3 D)zslopezisz3
17) yz=zx3z-z3x2z+z4,zxz=z3 17) z
A) slopezisz0 B)z slopezisz1 C)z slopez isz -9 D)z slopezisz9
18) yz=z-3z-zx3,zxz=z1 18) z
A) slopezisz0 B)zslopezisz3 C)zslopezisz-1 D)z slopezisz-3
3
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z z z z z z z z
Solvezthez problem.
19) Givenz z lim f(x)z=zLl,z z lim f(x)z=zLr,zandz Llz≠z Lr,zwhichzofzthezfollowingzstatementszisztrue? 19) z
x→0- x→0+
I. limz f(x)z=zLlz
x→0
II. limz f(x)z=zLrz
x→0
III. limz f(x)zdoesznotzexist.
zx→0
A) III B)z II C)z none D)z I
20) Givenz z lim f(x)z=zLl,z z lim f(x)z=z Lrz,zandzLlz=zLr,zwhichzofzthezfollowingzstatementsziszfalse? 20) z
x→0- x→0+
I. limz f(x)z=zLlz
x→0
II. limz f(x)z=zLrz
x→0
III. limz f(x)zdoesznotzexist.
zx→0
A) II B)z I C)z III D)z none
21) Ifz limz f(x)z=zL,zwhichzofzthezfollowingzexpressionszareztrue?z 21) z
x→0
I. limz f(x)zdoesznotzexist.
x→0-
II. limzx zf(x)zdoesznotzexist
→0+
III. limz .zf(x)z=zL
x→0-
f(x)z=zL
IV. limzx
→0+
A) IIzandzIIIzonly B)z IzandzIIzonly C)z IzandzIVzonly D)z IIIzandzIVzonly
22) Whatzconditions,zwhenzpresent,zarezsufficientztozconcludezthatzazfunctionzf(x)zhaszazlimitzaszxz 22) z
approacheszsomezvaluezofza?
A) Eitherzthezlimitzofzf(x)z aszx→az fromzthezleftzexistszorzthez limitzofzf(x)z aszx→az fromzthezrightzexists
B) f(a)zexists,zthezlimitzofzf(x)zaszx→azfromzthezleftzexists,zandzthezlimitzofzf(x)zaszx→azfromzthezrightz
exists.
C) Thezlimitzofzf(x)zaszx→azfromzthezleftzexists,zthezlimitzofzf(x)zaszx→azfromzthezrightzexists,zandzatzl
eastzonezofzthesezlimitsziszthezsamezaszf(a).
D) Thezlimitzofzf(x)zaszx→azfromzthezleftzexists,zthezlimitzofzf(x)zaszx→azfromzthezrightzexists,zandzt
heseztwozlimitszarezthezsame.
4
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