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mn ui bày mk nha củm mơn mn nhìu
NV
Nguyễn Việt Lâm
Giáo viên
2 tháng 11 2021
Tất cả k dưới đây là \(k\in Z\)
1.
ĐKXĐ: \(1-2cosx\ne0\Rightarrow cosx\ne\dfrac{1}{2}\)
\(\Rightarrow x\ne\pm\dfrac{\pi}{3}+k2\pi\)
2.
\(cos2x-1=0\Rightarrow cos2x=1\)
\(\Rightarrow2x=k2\pi\)
\(\Rightarrow x=k\pi\)
b.
\(\sqrt{3}cotx-3=0\Rightarrow cotx=\sqrt{3}\)
\(\Rightarrow x=\dfrac{\pi}{6}+k\pi\)
c.
\(2sin^22x+sin2x-1=0\)
\(\Rightarrow\left[{}\begin{matrix}sin2x=-1\\sin2x=\dfrac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}2x=-\dfrac{\pi}{2}+k2\pi\\2x=\dfrac{\pi}{6}+k2\pi\\2x=\dfrac{5\pi}{6}+k2\pi\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{\pi}{4}+k\pi\\x=\dfrac{\pi}{12}+k\pi\\x=\dfrac{5\pi}{12}+k\pi\end{matrix}\right.\)
3.
Theo điều kiện có nghiệm của pt lượng giác bậc nhất, pt đã cho có nghiệm khi:
\(\sqrt{3}^2+2^2\ge m^2\)
\(\Rightarrow m^2\le7\)
\(\Rightarrow-\sqrt{7}\le m\le\sqrt{7}\)
NV
Nguyễn Việt Lâm
Giáo viên
23 tháng 4 2022
1.
\(y'=\dfrac{3}{\left(x+2\right)^2}\Rightarrow\left\{{}\begin{matrix}y'\left(-1\right)=3\\y\left(-1\right)=-2\end{matrix}\right.\)
Phương trình tiếp tuyến:
\(y=3\left(x+1\right)-2\Leftrightarrow y=3x+1\)
2.
\(y'=2x+3\)
\(\Rightarrow\left\{{}\begin{matrix}y'\left(1\right)=5\\y\left(1\right)=2\end{matrix}\right.\)
Phương trình tiếp tuyến:
\(y=5\left(x-1\right)+2\Leftrightarrow y=5x-3\)
NV
Nguyễn Việt Lâm
Giáo viên
23 tháng 4 2022
3.
\(y'=\dfrac{-4}{\left(x-1\right)^2}\)
Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow\dfrac{x_0+3}{x_0-1}=2\Rightarrow x_0+3=2x_0-2\)
\(\Rightarrow x_0=5\)
\(\Rightarrow y'\left(5\right)=\dfrac{-4}{\left(5-1\right)^2}=-\dfrac{1}{4}\)
Phương trình tiếp tuyến:
\(y=-\dfrac{1}{4}\left(x-5\right)+2\Leftrightarrow y=-\dfrac{1}{4}x+\dfrac{13}{4}\)
4.
\(y'=2x+2\)
Gọi \(x_0\) là hoành độ tiếp điểm \(\Rightarrow x_0^2+2x_0+4=3\)
\(\Rightarrow x_0^2+2x_0+1=0\Rightarrow x_0=-1\)
\(\Rightarrow y'\left(-1\right)=2.\left(-1\right)+2=0\)
Tiếp tuyến:
\(y=0\left(x+1\right)+3\Leftrightarrow y=3\)
NV
Nguyễn Việt Lâm
Giáo viên
8 tháng 3 2021
\(=\lim\limits_{x\rightarrow0}\dfrac{\sqrt{4x+1}-\left(2x+1\right)+2x+1-\sqrt[3]{6x+1}}{x^2}\)
\(=\lim\limits_{x\rightarrow0}\dfrac{-\dfrac{4x^2}{\sqrt{4x+1}+2x+1}+\dfrac{x^2\left(8x+12\right)}{\left(2x+1\right)^2+\left(2x+1\right)\sqrt[3]{6x+1}+\sqrt[3]{\left(6x+1\right)^2}}}{x^2}\)
\(=\lim\limits_{x\rightarrow0}\left(-\dfrac{4}{\sqrt{4x+1}+2x+1}+\dfrac{8x+12}{\left(2x+1\right)^2+\left(2x+1\right)\sqrt[3]{6x+1}+\sqrt[3]{\left(6x+1\right)^2}}\right)\)
\(=\dfrac{-4}{1+1}+\dfrac{12}{1+1+1}=2\)
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