Giới hạn dãy số + hàm số ( tong hop)

... n + + + + + + = = = + + + 2 22222 ( 3 3 )( 3 3 )2) lim 3 3 lim ( 3 3 )333 3 3lim lim lim23 33 31 1n n n n n nn n nn n nnnn n nn n + + − + + + + + − = = + + + + + = = = + + + + ... lim4nn + + 5 13 / lim3 2nn− + 222 34 / lim2n nn n n + + + −22 35.lim1n nn n + + + ( 1 )(2 1)6.lim (3 2 )( 3)n nn n + − + + (2 )(3 )9.lim ( 1 )( 2)n n nn n + + + Bài ... = = + + + + + + 2 2222 ( 4 5 3 2 )( 4 5 3 2 )3) lim 4 5 3 2 lim4 5 3 23 3 3lim lim44 5 3 2n n n n n nn n nn n nnn n n + + − + + + + + − = + + + + = = + + + Bài 5 :Giới hạn trong...

... n n + − + − − + − + + − + − + − + + − − ( ) ( ) ( ) ( ) ( ) ( ) 2 2 5 2 3 2 3 1 10 4 3 ) lim )lim 3 2 1 4 1 3 3 n n n n g h n n n n + − − − − + − BT3: Tìm các giới hạn sau: ( ) ( ) ( ) ( ) 3 ... + + + + − + − + − − + − − ( ) 2 3 1 4 3 2 3 2 4 1 3 2 2 2 1 2 3 11 ) lim )lim ) lim )lim 7 6 9 6 8 11 3 2 4 4 n n n n n n n n e f g h n n n n n n n + + + + − + − + − − + − − − + + − + + ( ) ( ... x x x x x x x x + + + + + + − + − − = + − + − − = = + − +   + − +  ÷   − − = = =     + − + + − +  ÷  ÷     BÀI TẬP BT14: Tính các giới hạn sau: ( ) ( ) 2 2 )lim 2 4...

... 132lim/52 ++ + nnnn )3 )(2 3( )12 )(1 ( lim/6 ++ + nnnn 132lim/722 ++ + nnnn 132lim/8243 ++ nnn )2 )(1 ( )3 )(2 ( lim/9 ++ + nnnnn Bài tập 2: Tính các giới hạn: 112lim/122 + −nn ... có: u1 + u4 + u7 + u10 + u13 + u16 = 147 ⇔ (u1 + u16) + (u4 + u13) + (u7 + u10) = 147 ⇔ (2 u1 + 15d) + (2 u1 + 15d) + (2 u1 + 15d) = 147 ⇔ 3(2 u1 + 15d) ... 165.Giải:Gọi cấp số cộng là: ÷ u3 - 3d, u3 - d, u3, u3 + d, u3 + 2d Theo giả thiết ta có: ±==⇔ =++ ++ + + =++ ++ + + 25165) 2() ( )() 2( 25) 2() ( )() 2( 332323232333333dududuududududuududu...

... 7lim3 5n nn− + + a. 2/3 b. 0 c. -∞ d. Đáp án khácCâu 25: 222 15 11lim3 3n nn n− + − + a. 2/3 b. -2/3 c. -∞ d. + ∞Câu 26: ( ) ( )3 3 22 1 1 3lim7 5n nn n + − + −a. -6 b. ... 6 c. -∞ d. + ∞Câu 27: ( )2 2lim 2 3 1n n+ − + a. 2 b. 1 c. -∞ d. + ∞Câu 28:1lim1n n+ −a. 0 b. 1 c. -∞ d. + ∞Câu 29: 3 11lim1 7.2nn− + a. 0 b. 1 c. -∞ d. + ∞Câu 30: 12 ... 3/2 Câu 21: ( )4lim 50 11n n− − + a. -∞ b. + ∞ c. 1 d. – 1Câu 22: 3 2 3lim 7n n−a. -∞ b. + ∞ c. 1 d. – 1Câu 23: 33lim2 15n nn− + a. -1/2 b. 3/2 c. - ∞ d. + ∞Câu 24: 4...

... niệm giới hạn của dãy số và hàm số 1.2.3.1. Một số vấn đề về giới hạn vô cực của dãy số Ví dụ: Xét += + 2lim nn và += + nnqlim với q > 1. Nhng còn các giới hạn dãy số ( ) ( )21 ... niệm định nghĩa dãy có giới hạn, không phải mọi dãy số đều là hoặc có giới hạn hữu hạn ( L0 ) hoặc có giới hạn vô cực ( ), nếu dãy số nào có giới hạn hãy chỉ ra giới hạn của dãy số bằng cách ... 0 (0 %)3 2 (3 ,8%) 0 (0 %)4 0 (0 %) 3 (5 ,5%)5 7 (1 3,5%) 1 2(2 1,8% )6 7 (1 3,5%) 7 (1 2,7%)7 8 (1 5,4%) 15 (2 7,2%)8 10 (1 9,2%) 9 (1 6,4%)9 9 (1 7,3%) 5(9 ,1%)10 8 (1 7,3%) 4 (7 ,3%)11 1 (1 ,9%) 0 (0 %)...

... n = k+1, tức là cần chứng minh ( )21kh21)k(k1)h(k1h1 + ++ + + + Thật vậy ( ) ( ) ( ) ( )h1h21)k(kkh1h1h1h12k1k + − ++ ++ =+ + 21)hk(kkhhkh121)k(kh21)hk(kkhhkh122322− ++ ++ − + − ++ ++ ... dãy số, hàm số, giới hạn dãy số, giới hạn hàm số … 246. Thực trạng dạy học chủ đề giới hạn ở trường PT…………… 25Chương 2: Xây dựng hệ thống bài tập nâng cao chủ đề giới hạn dãy số, giới hạn hàm ... TẬP NÂNG CAO CHỦ ĐỀ GIỚI HẠN DÃY SỐ, GIỚI HẠN HÀM SỐ 2.1. Giới hạn dãy số 2.1.1. Một số bài tập điển hình về giới hạn dãy số SGK Đại số và Giải tích 11Ví dụ 1. Cho dãy số { }nu với nn3nu=a....

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... TẬP VỀ GIỚI HẠN DÃY SỐ - GIỚI HẠN HÀM SỐ I. Giới hạn dãy số: I.1. Các giới hạn cơ bản: 1. ( )001lim >=∞→ααnn 2. pnn pn∀=∞→,1lim 3. ( )01lim>=∞→αnna 4. ( )( )paannpn∀> =+ →,001lim ... Tính các giới hạn sau: 1. 11lim1−−→nmxxx 2. 131) 1() 1).. .(1 ) .(1 (lim−→−−−−nnxxxxx 3. 121lim22−−−∞→xxxx 4. xxxxx1)31 )(2 1 )(1 (lim0 ++ + 5. 5250)5 1() 1(limxxxxx ++ + 6. 13lim321− ++ →xxxxx ... yxxlnlim0→= )(ln)(lim0xuxvxx→=a thì [ ] )() (lim0xvxxxu→ = ea 3. [ ] )() (lim0xgxxxf→có dạng 1∞. Khi ñó: [ ] )() (lim0xgxxxf→ =( ) )(1 )(1 )(1 )1 )(( 1lim0xgxfxfxxxf−−→ += [ ] )(0 1)(limxgxxxfe−→ Bài...

... TẬP VỀ GIỚI HẠN DÃY SỐ - GIỚI HẠN HÀM SỐ I. Giới hạn dãy số: I.1. Các giới hạn cơ bản: 1. ( )001lim >=∞→ααnn 2. pnn pn∀=∞→,1lim 3. ( )01lim>=∞→αnna 4. ( )( )paannpn∀> =+ →,001lim ... Tính các giới hạn sau: 1. 11lim1−−→nmxxx 2. 131) 1() 1).. .(1 ) .(1 (lim−→−−−−nnxxxxx 3. 121lim22−−−∞→xxxx 4. xxxxx1)31 )(2 1 )(1 (lim0 ++ + 5. 5250)5 1() 1(limxxxxx ++ + 6. 13lim321− ++ →xxxxx ... yxxlnlim0→= )(ln)(lim0xuxvxx→=a thì [ ] )() (lim0xvxxxu→ = ea 3. [ ] )() (lim0xgxxxf→có dạng 1∞. Khi ñó: [ ] )() (lim0xgxxxf→ =( ) )(1 )(1 )(1 )1 )(( 1lim0xgxfxfxxxf−−→ += [ ] )(0 1)(limxgxxxfe−→ Bài...

... kỳ, kể từ một số hạng nào đó trở đi.Ký hiệu: hay khi - Dãy số (un) có giới hạn khi nếuKý hiệu: hay khi + n + limnu = + nu + n + n + lim( )nu = + limnu = nu n + 2. Mét vµi ... số dương bất kỳ, kể từ số hạng nào đó trở đi.9 10384.10 384.1010nnu n= > > IV/ Giới hạn ở vô cực 1. Định nghĩa- Ta nói dãy số (un) có giới hạn khi nếu un lớn hơn một số ... Phương pháp giải toán + Để tìm giới hạn dãy số ta thường đưa về các giới hạn đặc biệt và áp dụng các định lý về giới hạn vô cực. Để áp dụng các định lý nói trên, thông...