chuyÊn ĐỀ toÁn -...
TRANSCRIPT
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
1
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
CHUYN TON:
PHONG CCH LM CHUN CHO 1 BI TON KHO ST HM S, HNG DN TRNH BY P V C TH Y CC BC KHO ST. Chuyn i gii p thc mc khi cc em trnh by ton
kho st hm s, y cc trng hp v mi loi hm s.
Cc v d u nm trong sch gio khoa c bn. Cc em hy c v cho kin ng gp v ch gio qua
nick fb: Gia s Bi Thi: MC LC:
- Hm s bc 3.2->7. - Hm trng phng7->9. - Hm s dng a thc bc nht trn bc nht9->11 - Hm s dng a thc bc 2 trn bc nht.11->HT.
Trn Mu T-TMT
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
2
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
CC V D C TH CHO PHONG CCH TRNH BY. Hm bc 3. Bi 1: KHO ST V V TH HM S Y =3 + 3 4 Li gii: 1. TX: D = R 2. S bin thin.
- Chiu bin thin: + ao hm y' = 3 + 6
y' = 0 0
2
x
x
Ta c du ca y:
: + Do : Hm s ng bin trn khong (,2)(0,+) Hm s nghch bin trn (-2,0).
- Cc tr ca hm s: + Hm s t cc i ti x = -2, yC = 0. + Hm s t cc tiu ti x = 0 , yCT = -4
- Gii hn hm s:
+ 3 2 3
3
3 4lim lim( 3 4) lim (1 )x x x
y x x xx x
+ 3 2 3
3
3 4lim lim ( 3 4) lim (1 )x x x
y x x xx x
- th hm s khng c tim cn. - Bng bin thin.
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
3
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
3. th ca hm s: - Giao im ca th vi cc trc ta : + Giao diem cua ham so voi truc Ox y = 0 x = -2 ; x = 1 + Giao diem cua ham so voi truc Oy x = 0 y = -4
- Nhan xet: + Do thi ham so nhan diem uon E( 0 ; -4 ) lam tam doi xung
- Ve do thi ham so:
Li bnh: Phng php trnh bay trn l cch trnh by chun v y nht cho bi ton, khi c cc em c th thy hi di, nhng khi lm thnh tho v nh cc bc th cc em thng lm bi ny trong vng 5 pht l xong. Ngoi ra khi v th cc em c th tm thm cc im ngoi nhp v th cho d khng cn trnh by vo bi lm, trn l cch trnh by rt chun ri.
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
4
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
Bi 2: KHO ST HM S V V TH HM S Y =
+ 2
Li gii:
1. TX: D = R. 2. S bin thin : - Chiu bin thin:
+ o hm: y = + 2 2
y=0< => + 2 2 = 0 1 3
1 3
Ta c du ca y:
+ Do : Hm s ng bin trn khong (-,1 + 3)(1 + 3,+)
Hm s nghch bin trn khong (1 3,1 + 3) - Cc tr ca hm s:
+Hm s t cc i ti x = 1 3 v yC = y(1 3) = 2 + 23
+Hm s t cc tiu ti x = 1 + 3 v yCT = y(1 + 3) = 2 23 - Gii hn hm s:
+ 3 2 3
2 3
1 2 1 1 2 2lim lim( 2 ) lim ( )
3 3 3 3x x xy x x x x
x x x
+3 2 3
2 3
1 2 1 1 2 2lim lim( 2 ) lim ( )
3 3 3 3x x xy x x x x
x x x .
- Hm s khng c tim cn. - Bng bin thin.
3. th ca ca hm s:
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
5
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
- th giao vi cc trc:
+ Giao vi ox:
+ 2
= 0 c 3 nghim , do th ct ox
ti 3 im phn bit.
+ Giao vi oy: x= 0 => y =
, do hm s ct trc oy ti im ( 0,
)
- Hm s nhn (-1,2) lm im un. - Ta c th hm s .
Li bnh: Bi ton ny a ra nhm cung cp cho cc em v vic 1 s bi ton cho s liu khng c p th cc em khng nht thit phi tm ra kt qu, v d nh phn tm giao im ca th vi ox, cc em ch cn ni n ct trc ox ti 3 im phn bit l c, v phn cc tr hm s cng vy
cc em khng cn tm ra kt qu l yC = y(1 3) = 2 + 23 yCT =
y(1 + 3) = 2 23,ch cn vit
yC = y(1 3)yCT = y(1 + 3) cng c cc em .
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
6
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
Bi 3: KHO ST V V TH CA HM S y= 3 + 3 + 1 Li gii:
1. TX: D=R 2. S bin thin: - Chiu bin thin:
+ o hm: y = 3 6 + 3 y = 0 3 6 + 3 = 0 x = 1. Suy ra y = 3( 1) 0, . Do hm s lun ng bin trn R.
- Hm s khng c trc tr. - Gii hn:
+ 23 2 3
3
3 3 1lim lim ( ) l3 3 1 im (1 )x x x
y xx
x xx x
x
+ 23 2 3
3
3 3 1lim lim( ) l3 3 1 im (1 )x x x
y xx
x xx x
x
- Hm s khng c tim cn. - Bng bin thin.
3. th ca hm s. - th giao vi cc trc ta .
+ Giao vi ox: 3 + 3 + 1 = 01, 01m
+ Giao vi oy: x = 0=> y = 1, do th ct oy ti im (0,1) - th h/s nhn im ( 1, 2) lm tm i xng. - Ta c th ca hm s.
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
7
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
Li bnh: Trn l 3 bi ton vi 3 trng hp hon ton khc nhau, cc em thy c s trnh by y v theo tun t nh th, l 3 bi ton in hnh cho vic kho st hm s bc 3. Sau y chng ta chuyn sang hm s mi.
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
8
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
HM TRNG PHNG. Bi 4. KHO ST V V TH HM S y = + 2 2 Li gii:
1. TX: D=R 2. S bin thin: - Chiu bin thin:
+ o hm: y = 4 + 4
y = 0 4 + 4 = 0
0
1
1
x
x
x
Ta c du ca y:
+ Do : Hm s ng bin trn khong (-,1)(0,1) Hm s nghch bin trn khong (-1,0) v (1,+)
- Cc tr ca hm s. + Hm s t cc i ti 2 im c honh x = -1, yC=-1.V x = 1,yC=-1 +Hm s t cc tiu ti im c honh x=0, yCT=-2.
- Gii hn hm s:
+4 4
2 4
22 2)2 2
lim lim ( lim ( 1 )x x x
y xxx x
x
+4 4
2 4
22 2)2 2
lim lim ( lim ( 1 )x x x
y xxx x
x
- Hm s khng c tim cn. - Bng bin thin:
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
9
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
3. th ca hm s. - Giao diem cua do thi voi cac truc toa do
+ Giao diem cua ham so voi truc Ox y = 0 Vo nghiem, ham so khong cat truc Ox
+ Giao diem cua ham so voi truc Oy x = 0 y = -2, do o ham so ct oy to im (0,-2) - Nhan xet + Ham so da cho la ham so chan nen do thi nhan truc tung lam truc doi xung -Ve do thi ham so.
Li bnh: Cc bi ton hm trng phng u c cch trnh by nh th, cc em trnh by v lm nhiu th s thnh tho v lm rt nhanh, cc trng hp s liu khng p th cc em cng lm theo hng dn ca anh trang th 5 ca chuyn ny. Tip theo ta sang dng hm s khc.
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
10
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
HM S DNG A THC BC NHT TRN BC NHT.
Bi 5: KHO ST V V TH CA HM S y =
.
Li gii:
1. TX: D = R1
\2
.
2. S bin thin: - Chiu bin thin:
+ o hm:
y =
() , ta thy y >0, .
+ Do hm s lun ng bin trn khong (-,
)(
, +).
- Hm s khng c cc tr. - Gii hn hm s:
1 1( ) ( )
2 2
1 1( ) ( )
2 2
2 1lim lim
2 1 2
2 1lim lim
2 1 2
2lim lim
2 1
2lim lim
2 1
x x
x x
x x
x x
xy
x
xy
x
xy
x
xy
x
- Tim cn ca hm s:
Do: 1
lim lim2x x
y y
, nn hm s c tim cn ngang l t y=
.
Do:
1( )
2
1( )
2
lim
lim
x
x
y
y
nn hm s c tin cn ng l t x = -
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
11
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
- Bng bin thin:
3. th hm s: - th giao vi cc trc ta .
+ Trc ox: ti im (2,0) + Trc oy ti im (2,0)
- th nhn giao im (
,
) lm tm i xng.
- Ta c th ca hm s.
Li bnh: Trn l cch trnh by ca dng hm s trn, cc em hon ton lm tun t nh th cho cc bi ton khc.
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
12
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
HM S DNG A THC BC 2 TRN BC NHT
Bi 6: KHO ST V V TH HM S y =
Li gii:
Ta c: y =
= + 1 +
1. TX: D = R \ 1 .
2. S bin thin: - Chiu bin thin:
+ o hm:
y = 1
().
y = 0 1
()= 0
0
2
x
x
Ta c du ca y:
+ Do : Hm s ng bin trn khong (-,2)(0,+). Hm s nghch bin trn khong (-2,0).
- Cc tr ca hm s: + Ham so dat cuc dai tai diem x = -2; gia tri cuc dai cua ham so la y = -2 + Ham so dat cuc tieu tai diem x = 0; gia tri cuc tieu cua ham so la y = 2
- Gii hn ca hm s:
( 1)
2
( 1)
(
2
1) ( 1
2
)
2
2 2
1
2
lim lim
lim lim
lim lim
lim li
2
1
2 2
1
2m
2
1
x x
x x
x x
x x
y
y
y
x x
x
x x
x
x x
x
xy
x
x
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
13
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
- Tim cn ca th hm s. th hs khng c tim cn ngang.
Do: ( 1 )
( 1 )
l im
l im
x
x
y
y
nn th hm s c tim cn ng x = -1.
Gi tim cn xin l y = a. x+b.
Trong a =
2 2 21
(lim li
)m
1x xxy
x
x
x x
b =
2 2 2lim( . ) lim( l
2)
1im 1
1x x xx x x
y ax
xx
x
Do th hs c tim cn xin y = x +1 - Bng bin thin:
3. th ca hm s. - Giao diem cua do thi voi cac truc toa do
+ Giao diem cua ham so voi truc Ox y = 0 Vo nghiem, ham so khong cat truc Ox + Giao diem cua ham so voi truc Oy x = 0 y = 2
- Nhan xet + Do thi ham so nhan giao diem C (-1;0) cua 2 tiem can lam tam doi xung
- Ve do thi ham so:
-
Trn Mu T-TMT- CLB Gia S Bi Thi Khoa Hc: https://www.facebook.com/giasubaithikhoahoc?fref=ts.
14
VIC HC NH I THUYN NGC NC-KHNG TIN T S LI.
Li bnh: Nh vy chng ta tri qua cc v d tip cn c phng php v cch trnh by loi ton kho st hm s. Mong cc em ng gp kin qua nick fb: Gia S Khoa Hc. https://www.facebook.com/profile.php?id=100008341510957. -HT-