b. Because the kitchen is a dangerous place.

c. Because it only takes one match to cause a fire.

d. Because we electricity can kill.

e. Because we want to keep our children safe. (?)

a/ \(\lim\limits_{x\rightarrow3}\dfrac{\sqrt[3]{x^2-1}-2}{x-3}+\lim\limits_{x\rightarrow3}\dfrac{2-\sqrt[4]{1+5x}}{x-3}\)

\(=\lim\limits_{x\rightarrow3}\dfrac{x^2-1-8}{\left(x-3\right)\left(\sqrt[3]{\left(x^2-1\right)^2}+2.\sqrt[3]{x^2-1}+4\right)}+\lim\limits_{x\rightarrow3}\dfrac{16-1-5x}{\left(x-3\right)\left(\sqrt[4]{\left(1+5x\right)^3}+2\sqrt[3]{\left(1+5x\right)^2}+4.\sqrt[3]{1+5x}+8\right)}\)

\(=\lim\limits_{x\rightarrow3}\dfrac{\left(x-3\right)\left(x+3\right)}{\left(x-3\right)\left(\sqrt[3]{\left(x^2-1\right)^2}+2.\sqrt[3]{x^2-1}+4\right)}+\lim\limits_{x\rightarrow3}\dfrac{-5\left(x-3\right)}{\left(x-3\right)\left(\sqrt[4]{\left(1+5x\right)^3}+2\sqrt[3]{\left(1+5x\right)^2}+4\sqrt[3]{1+5x}+8\right)}\)

\(=\dfrac{3+3}{\sqrt[3]{\left(3^2-1\right)^2}+2.\sqrt[3]{3^2-1}+4}-\dfrac{5}{\sqrt[4]{\left(1+5.3\right)^3}+2\sqrt[3]{\left(1+5.3\right)^2}+4.\sqrt[3]{1+5.3}+8}=\dfrac{11}{32}\)

\(\Rightarrow a^2+b^2=1145\)

40/ 

\(L=\lim\limits_{x\rightarrow0}\dfrac{af\left(x\right)+b^n-b^n}{f\left(x\right)\left[\sqrt[n]{\left(af\left(x\right)+b^n\right)^{n-1}}+b.\sqrt[n]{\left(af\left(x\right)+b^n\right)^{n-2}}+....+b^{n-1}\right]}\)

\(L=\lim\limits_{x\rightarrow0}\dfrac{a}{\sqrt[n]{\left(af\left(x\right)+b^n\right)^{n-1}}+b.\sqrt[n]{\left(af\left(x\right)+b^n\right)^{n-2}}+...+b^{n-1}}\)

\(L=\lim\limits_{x\rightarrow0}\dfrac{a}{b^{n-1}+b^{n-1}++...+b^{n-1}}=\dfrac{a}{nb^{n-1}}\)

40/ 

\(\sqrt{1+ax}.\sqrt[3]{1+bx}+\sqrt[4]{1+cx}-1=\left(\sqrt{1+ax}-1\right)+\sqrt{1+ax}\left(\sqrt[3]{1+bx}-1\right)+\sqrt{1+ax}.\sqrt[3]{1+bx}.\left(\sqrt[4]{1+cx}-1\right)\)

\(=\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+ax}-1}{x}+\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+ax}\left(\sqrt[3]{1+bx}-1\right)}{x}+\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+ax}.\sqrt[3]{1+bx}\left(\sqrt[4]{1+cx}-1\right)}{x}\)

\(I_1=\lim\limits_{x\rightarrow0}\dfrac{1+ax-1}{x\left(\sqrt{1+ax}+1\right)}=\dfrac{a}{\sqrt{1+ax}+1}=\dfrac{a}{2}\)

\(I_2=\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+ax}\left(1+bx-1\right)}{x\left(\sqrt[3]{\left(1+bx\right)^2}+\sqrt[3]{1+bx}+1\right)}=\dfrac{b\sqrt{1+ax}}{\sqrt[3]{\left(1+bx\right)^2+\sqrt[3]{1+bx}+1}}=\dfrac{b}{3}\)

\(I_3=\lim\limits_{x\rightarrow0}\dfrac{\sqrt{1+ax}\sqrt[3]{1+bx}\left(1+cx-1\right)}{x\left(\sqrt[4]{\left(1+cx\right)^3}+\sqrt[3]{\left(1+cx\right)^2}+\sqrt[3]{1+cx}+1\right)}=\dfrac{c}{4}\)

\(\Rightarrow L=\dfrac{a}{2}+\dfrac{b}{3}+\dfrac{c}{4}\)

P/s: Thông cảm mình đang đau đầu nên làm hơi lâu :b

Hai tam giác vuông OHD và OBD bằng nhau (cạnh huyền - góc nhọn) nên suy ra OH=OB

Bài 20:

a, Độ dài cạnh còn lại của mảnh đất:

350 : 14 = 25 (m)

Chu vi mảnh đất:

2 x (14+25)= 78 (m)

b, Đổi: 15dm= 1,5m

Diện tích đất trồng cỏ:

1,5 x 25 x 2 + (14 - 1,5 x 2) x 1,5 x 2 = 108 (m²)

Diện tích mảnh đất:

25 x 14 = 350(m²)

Diện tích làm nhà:

350 - 108 = 242 (m²)

Đ.số:......