Luyện đề tháng 4

M

magiciancandy

Câu1b:Ta có:Tiệm cận đứng là đường thẳng x-3=0(d1)
Tiệm cận ngang là đường thẳng y-1=0(d2)
Gọi M(m;[TEX]\frac{m+2}{m-3}[/TEX])(\forallm#3)
=>d(M;(d1))=[TEX]\left|m-3 \right|[/TEX]
d(M;(d2))=[TEX]\left|\frac{m+2}{m-3}-1\right|[/TEX]
Theo đề bài ra :[TEX]\left|m-3 \right|[/TEX]=[TEX]\frac{1}{5}[/TEX][TEX]\left|\frac{m+2}{m-3}-1\right|[/TEX]=>m=+-2[TEX]\sqrt{2}[/TEX] hoặc m=4 hoặc m=2.
KL
 
M

magiciancandy

Câu4:I=[TEX]\int_{0}^{1}[/TEX]xln(1+[TEX]x^2[/TEX])dx
Đặt t=1+[TEX]x^2[/TEX]=>dt=2xdx
Đổi cận: x=0=>t=1
x=1=>t=2
=>I=[TEX]\frac{1}{2}\int_{0}^{1}lntdt[/TEX]
Đặt u=lnt du=[TEX]\frac{1}{t}dt[/TEX]
dv=dt => v=t
=>I=2ln2-[TEX]\int_{1}^{2}tdt[/TEX]=>I=2ln2-[TEX]\frac{3}{2}[/TEX]
 
M

magiciancandy

8b,Phương trình đường thẳng d dưới dạng tham số:[TEX]\left\{\begin{matrix} & & \\ x=2+t' & & \\ y=1-t' & & \\ z=1+2t' & & \end{matrix}\right.[/TEX]
Gọi véc tơ ud,véc tơ ud' lần lượt là hai VTPT của đường thẳng d và d'=>véc tơ ud(1;-1;2) và ud'(1;-1;1)=>[TEX]\left<ud,ud' \right>[/TEX]=(1;1;0)
Gọi A [TEX]\in [/TEX]d=>A(2;1;1)
B [TEX]\in [/TEX]d'=>B(4;2;0)
=>véc tơ AB(2;1;-1)=>[TEX]\left<ud,ud' \right>[/TEX]véc tơ AB=3#0=>d và d' chéo nhau
Gọi Q(2+t';1-t';1+2t')là điểm thuộc d
P(4+t;2-t;t) là điểm thuộc d'
=>véc tơ PQ (2+t-t';-t+t'+1;t-2t'-1)
Để PQ là đoạn vuông góc chung của d và d' thì VTCP PQ=[TEX]\left<ud,ud' \right>[/TEX]=(1;1;0)
=>[TEX]\left\{\begin{matrix} & & \\ 2+t-t'=1 & & \\ -t+t'+1=1 & & \\ t-2t'-1=0 & & \end{matrix}\right.[/TEX]
<=>[TEX]\left\{\begin{matrix} & & \\ t=-1 & & \\ t'=-1 & & \end{matrix}\right.[/TEX]=>PQ=[TEX]\sqrt{5}[/TEX]
 
Last edited by a moderator:
M

magiciancandy

7b,Ta có :I(1;2) là tâm đường tròn(C);R=3=>IM=IN=3
=>AI=[TEX]\sqrt{10}[/TEX]=>AN=1
Do S AMN=2S AIN=2[TEX]\frac{1}{2}[/TEX].AI.AN=[TEX]\sqrt{10}[/TEX]
 
M

magiciancandy

Câu2:Kết quả x=[TEX]\frac{k\Pi }{4}[/TEX]và x=k2pi............................
 
M

magiciancandy

Câu5 :hình như đề sai ạ.......................... .........................................................
 
M

magiciancandy

Nhưng đề cho là AK vuông vs SC và cắt SB tại H cơ mà.Ah,cậu cho tớ hỏi luôn là khi thi ĐH thì vẫn phải chứng minh công thức tính tỉ lệ thể tích hay được áp dụng luôn?
 
N

nguyenbahiep1

Nhưng đề cho là AK vuông vs SC và cắt SB tại H cơ mà.Ah,cậu cho tớ hỏi luôn là khi thi ĐH thì vẫn phải chứng minh công thức tính tỉ lệ thể tích hay được áp dụng luôn?

làm gì có câu nào trong đề như thế

đề ghi rất rõ ràng là

mặt phẳng (P) vuông với SC tại H

mặt phẳng (P) cắt SB tại K

làm gì có ý nào như ý của em

Khi đi thi em cần chứng minh lại công thức tỷ lệ thể tích này
 
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nguyenbahiep1

Chứng minh bài tổng quát hay chứng minh luôn trong bài tập mà đề cho ?Tiện thể cậu CM luôn cho tớ với:D

Tôi hơn em đến 5 tuổi đấy cậu tớ gì ở đây

[laTEX]\frac{V_{SAHK}}{V_{SABC}} = \frac{V_{A.SHK}}{V_{A.SBC}} \\ \\ \frac{V_{SAHK}}{V_{SABC}} = \frac{\frac{1}{3}h_A.S_{SHK}}{\frac{1}{3}h_A.S_{SBC}} \\ \\ \frac{V_{SAHK}}{V_{SABC}} = \frac{\frac{1}{2}SH.SK.sinS}{\frac{1}{2}SB.SC.sinS} \\ \\ \frac{V_{SAHK}}{V_{SABC}} = \frac{SH.SK}{SB.SC}[/laTEX]
 
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M

magiciancandy

Tôi hơn em đến 5 tuổi đấy cậu tớ gì ở đây

[laTEX]\frac{V_{SAHK}}{V_{SABC}} = \frac{V_{A.SHK}}{V_{A.SBC}} \\ \\ \frac{V_{SAHK}}{V_{SABC}} = \frac{\frac{1}{3}h_A.S_{SHK}}{\frac{1}{3}h_A.S_{SBC}} \\ \\ \frac{V_{SAHK}}{V_{SABC}} = \frac{\frac{1}{2}SH.SK.sinS}{\frac{1}{2}SB.SC.sinS} \\ \\ \frac{V_{SAHK}}{V_{SABC}} = \frac{SH.SK}{SB.SC}[/laTEX]

Tức là chứng minh cụ thể trong bài luôn à,thế nếu tớ chứng minh tổng quát có được không
 
F

fainkelia

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M

magiciancandy

Câu 6: Ta có: x=1-y
=>P=[TEX]\left[\left((1-y)^2+\frac{1}{y^2} \right) \right]\left[y^2+\frac{1}{(1-y)^2} \right][/TEX]
=>P=[TEX]y^2(1-y)^2+2+\frac{1}{y^2(1-y^2)}[/TEX]\geq4
=>MinP=4
 
E

enercedyslerewzk82

louis vuitton kyc48

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chenxj

exepteplawn

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huyentrang1801

câu lượng giác :
bạn chỉ cần phân tích $$2\sin x (1-\ cos x^2) +(-2 \cos x ^2 +\ cos x +1 ) =0 $$
rồi đặt nhân tử chung là ra .
câu số phức :
bạn đặt z = a+bi
$z^2=a^2-b^2+2abi $

$\mid z \mid=\sqrt[]{a^2+b^2}$
theo bài ra : $z^2+\mid z \mid =0$
thay vào cho phần thực và phần ảo bằng không
tìm ra [tex]\left[\begin {z=0}\\{z=i}\\{z=-i}[/tex]
 
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huyentrang1801

thầy ơi ! cho em hỏi thầy có thể định kì 1 khoảng thởi gian như 1 tuần đăng 1 đề đến cuối tuần nêu ra đáp án và nhận xét cách giải của từng bạn và chỉnh sửa được không ạ ! em rất kém trong phần trình bày nên rất mong được hoc hỏi thêm từ thầy và các bạn .
em cảm ơn thầy rất nhiều .
 
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