This document presents a direct comparison test theorem for determining if a series converges or diverges. It states that if the sequence of partial sums of another series AN is convergent, and the terms of the series an are less than or equal to the corresponding terms of AN for all n, then the series of an must also converge. It then provides a proof of this theorem showing that if the sequence of partial sums of AN approaches 0 as n and m approach infinity, then the sequence of partial sums of an must also approach 0, and therefore an converges.
This document presents a direct comparison test theorem for determining if a series converges or diverges. It states that if the sequence of partial sums of another series AN is convergent, and the terms of the series an are less than or equal to the corresponding terms of AN for all n, then the series of an must also converge. It then provides a proof of this theorem showing that if the sequence of partial sums of AN approaches 0 as n and m approach infinity, then the sequence of partial sums of an must also approach 0, and therefore an converges.
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Unique Advertising là công ty quảng cáo ngoài trời cung cấp dịch vụ quảng cáo trên pano, xe buýt,taxi, sản xuất quảng cáo, in ấn uy tín hàng đầu tại Hà Nội.
Allan Allsopp has over 35 years of experience as a landscape designer and manager. One project example is the 292 acre Beddington Farm Lands site, which involved excavating treated sewage and gravel to create a new landform incorporating water sports facilities and wildlife habitats. Another example is the 50 acre Sandhills Primary School site in Oxford, where Allan Allsopp designed features like woodlands, ponds, sports pitches and play areas. A third example is managing construction of a private 1 acre garden in Oxfordshire incorporating design elements like courtyard pools and planting features.
Uso responsable de las tic's recomienda no compartir información de cuentas, evitar aceptar solicitudes de extraños porque sus intenciones son desconocidas, y siempre tener una copia de contraseñas e información fundamental para proteger la privacidad.
ความสุจริตทางวิชาการ เชื่อมไทยเชื่อมโลก Connect Thailand, Connect the World in The “Academic Honesty”
With Five Tools to Drive The Universities to Build The Smart Graduates
With Integrity
![Calculus I The Newtun Page 1
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☺ รักวัวใหผูก รักลูกใหตัง....มาเรียนพิเศษ @ The Newtun ☺ By P’tun
แบบฝกหัดฝกพลังยุทธ
1. จงวาดกราฟตอไปนี้
1.1
>+−
≤+−
=
2,2
2,1|12|
xx
xx
y 1.2 1,2 2
−=+= txty
2. จงหาลิมิตตอไปนี้
2.1
x
xx
x
++−
→
11
lim
2
0
(1) 2.2
26
14
lim 2
2
2
1
−−
−
−→ xx
x
x
ตอบ 4/7
2.3 22 6
2
lim
xx
x
x −−
−
−
→
ตอบ 1/5 2.4
2
44
lim
2
2 −
+−
→ x
xx
x
ตอบ หาคาไมได+ ขวาไม
เทากัน
2.5
32
52
lim
2
2
−+−
++
∞−→
xxx
xx
x
ตอบ 2.6
xx
xxx
x sin
2sinsin22
lim
3
0
−+
→
ตอบ 0
3. กําหนด
−<
−≥
+
−
=
3,
3
1
3,
2
3
)(
x
x
x
x
xf จงตรวจดูวาฟ2งก3ชัน f(x) มีความตอเนื่องที่ x = 3 หรือไม
4. จงวาดกราฟตอไปนี้โดยใช+ลิมิต
322
3
−−
=
xx
x
y
5. จงหาอนุพันธ3 (dy/dx)
5.1 ( ) 5
5101010ln)52(3
2 33
3.2
x
xx
x
y −+−−+
−
=
π
5.2 )3tansin( π⋅= x
ey 5.3
2
)31tan(
7 xx
y +−
=
5.4 3
)(
1
cos2ln x
x
y ⋅
−= 5.5 )csc
2
(cosh199
x
x
y +=
5.6 )harctan(cos xy = 5.7 2014tan =+−+ yeyxy x
5.8 [ ] ( )1ln
)cos(ln
−
=
x
xy 5.9 1+= xy จงหา )1(' −f โดยใช+นิยาม
6. จงหา ( )( )yf
'1−
ของ yyxx =−+ 223
7. กําหนดให+ txty =+= ,42 จงหา 2
2
dx
yd
ที่จุด t = 1
8. จงหาเส+นสัมผัสและเส+นตั้งฉากกับเส+นโค+งที่ผานจุดที่กําหนด xy cos2= เมื่อ
4
π
=x
9. จงประมาณคา 3
9.262 −+=y](https://image.slidesharecdn.com/calculusiproblem-150818070635-lva1-app6891/85/Calculus-i-problem-1-320.jpg)
