Giúp mình bài 2
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
tiêu đề bài hai có nghĩa là j zậy bnnnnnnnnnnnnnnnn
mk nhát đọc đề quá
Bài 1:
a: Xét ΔABI và ΔACI có
AB=AC
AI chung
BI=CI
Do đó: ΔABI=ΔACI
2.
\(cosx+cos3x=1+\sqrt{2}sin\left(2x+\dfrac{\pi}{4}\right)\)
\(\Leftrightarrow2cos2x.cosx=1+cos2x+sin2x\)
\(\Leftrightarrow2cos2x.cosx=2cos^2x+2sinx.cosx\)
\(\Leftrightarrow cosx\left(cos2x-cosx-sinx\right)=0\)
\(\Leftrightarrow cosx\left(cos^2x-sin^2x-cosx-sinx\right)=0\)
\(\Leftrightarrow cosx\left(cosx+sinx\right)\left(cosx-sinx-1\right)=0\)
\(\Leftrightarrow cosx.\sqrt{2}sin\left(x+\dfrac{\pi}{4}\right).\left[\sqrt{2}cos\left(x+\dfrac{\pi}{4}\right)-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sin\left(x+\dfrac{\pi}{4}\right)=0\\cos\left(x+\dfrac{\pi}{4}\right)=\dfrac{1}{\sqrt{2}}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=-\dfrac{\pi}{4}+k\pi\\x+\dfrac{\pi}{4}=\pm\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{2}+k\pi\\x=-\dfrac{\pi}{4}+k\pi\\x=k2\pi\end{matrix}\right.\)
\(\lim\limits_{x\rightarrow4}\dfrac{2x-8}{4x^2-18x+8}=\lim\limits_{x\rightarrow4}\dfrac{2\left(x-4\right)}{2\left(x-4\right)\left(2x-1\right)}=\lim\limits_{x\rightarrow4}\dfrac{1}{2x-1}=-\dfrac{1}{7}\)
b.
\(\lim\limits_{x\rightarrow-\infty}\left(\sqrt{x^2+3x-1}+x\right)=\lim\limits_{x\rightarrow-\infty}\dfrac{\left(\sqrt{x^2+3x-1}+x\right)\left(\sqrt{x^2+3x-1}-x\right)}{\sqrt{x^2+3x-1}-x}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{3x-1}{\sqrt{x^2+3x-1}-x}=\lim\limits_{x\rightarrow-\infty}\dfrac{3-\dfrac{1}{x}}{-\sqrt{1+\dfrac{3}{x}-\dfrac{1}{x^2}}-1}=\dfrac{3-0}{-\sqrt{1+0-0}-1}=-\dfrac{3}{2}\)
c.
\(\lim\limits_{x\rightarrow1^+}\dfrac{2x^2-3x+1}{x^2-1}=\lim\limits_{x\rightarrow1^+}\dfrac{\left(x-1\right)\left(2x-1\right)}{\left(x-1\right)\left(x+1\right)}=\lim\limits_{x\rightarrow1^+}\dfrac{2x-1}{x+1}=\dfrac{1}{2}\)
d.
\(\lim\limits_{x\rightarrow-\infty}\dfrac{2x^2+3x}{\sqrt{4x^4+2x^2}+3x^2-1}=\lim\limits_{x\rightarrow-\infty}\dfrac{x^2\left(2+\dfrac{3}{x}\right)}{x^2\left(\sqrt{4+\dfrac{2}{x^2}}+3-\dfrac{1}{x^2}\right)}\)
\(=\lim\limits_{x\rightarrow-\infty}\dfrac{2+\dfrac{3}{x}}{\sqrt{4+\dfrac{2}{x^2}}+3-\dfrac{1}{x^2}}=\dfrac{2+0}{\sqrt{4+0}+3-0}=\dfrac{2}{5}\)