Giúp e với ạ, e cảm ơn
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\(B=x^2+0,2x+1,01=\left(x+0,1\right)^2+1\)
Tại \(x=0,9\)thì: \(B=\left(0,9+0,1\right)^2+1=2\)
\(C=x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
Tại \(x=3,5;\)\(y=3,25\)thì: \(C=\left(3,5-2\times3,25\right)\left(3,5+2\times3,25\right)=-30\)
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\(M=\left(5x-3y+3xy+x^2y^2\right)-\left(\dfrac{1}{2}x+2xy-y+4x^2y^2\right)\)
\(=5x-3y+3xy+x^2y^2-\dfrac{1}{2}x-2xy+y-4x^2y^2\)
\(=\left(5x-\dfrac{1}{2}x\right)+\left(y-3y\right)+\left(3xy-2xy\right)+\left(x^2y^2-4x^2y^2\right)\) \(=4,5x-2y+xy-3x^2y^2\)
Thay \(x=1;y=-\dfrac{1}{2}\) vào ta có:
\(4,5x-2y+xy-3x^2y^2\)
\(=4,5.1-2.\left(-\dfrac{1}{2}\right)+1.\left(-\dfrac{1}{2}\right)-3.1^2.\left(-\dfrac{1}{2}\right)^2\)
\(=4,5+1-\dfrac{1}{2}-\dfrac{3}{4}\) \(=\dfrac{17}{4}\)
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8 It took me 3 hours to do these exercise
9 Many years ago, my village used to be very poor
10 Mary last met him 5 years ago
11 Would you mind giving me a hand
12 There used to be many old buildings in this city
13 When were they married
14 I started learning Japanese 2 years ago
15 Jack used to be a good student
16 My sister used to buy all her clothes in Henry's
17 Braille is reading system for the blind
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Cách làm ngắn gọn: \(5=\dfrac{5\left(x-1\right)}{x-1}=\dfrac{5x-5}{x-1}=\dfrac{5x+5-10}{x-1}\)
Do đó chọn \(f\left(x\right)=5x+5\) thế vào nhanh chóng tính ra kết quả giới hạn
Còn cách khác phức tạp hơn (có thể sử dụng cho tự luận):
Do \(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-10}{x-1}=5\) hữu hạn nên \(f\left(x\right)-10=0\) có nghiệm \(x=1\)
\(\Rightarrow f\left(1\right)-10=0\Rightarrow f\left(1\right)=10\)
Do đó:
\(\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-10}{\left(\sqrt{x}-1\right)\left(\sqrt{4f\left(x\right)+9}+3\right)}=\lim\limits_{x\rightarrow1}\dfrac{\left[f\left(x\right)-10\right]\left(\sqrt{x}+1\right)}{\left(x-1\right)\left(\sqrt{4f\left(x\right)+9}+3\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{f\left(x\right)-10}{x-1}.\dfrac{\sqrt{x}+1}{\sqrt{4f\left(x\right)+9}+3}=5.\dfrac{1+1}{\sqrt{4f\left(1\right)+9}+3}=5.\dfrac{2}{\sqrt{4.10+9}+3}=...\)
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