tìm x biết : \(5^{2x-3}-2.5^2=75\)
\(\left(3.\left|x.\left(-24\right).7^{2019}\right|\right)=2.7^{2020}.\frac{1}{2020}\)
tìm x biết \(\left(3.\left|x.\left(-24\right)\right|.7^{2019}\right)=2.7^{2020}.\frac{1}{2020}\)
tìm x biết
\(\frac{\left(2019-x^2\right)+\left(2019-x\right)\left(x-2020\right)+\left(x-2020\right)^2}{\left(2019-x\right)^2-\left(2019-x\right)\left(x-2020\right)+\left(x-2020^2\right)}\) = \(\frac{19}{49}\)
Tìm x biết \(\frac{\left(2019-x\right)^2+\left(2019-x\right)\left(x-2020\right)}{\left(2019-x\right)^2-\left(2019-x\right)\left(x-2020\right)}\)\(\frac{+\left(x-2020\right)^2}{+\left(x-2020\right)^2}\)\(=\frac{19}{49}\)
Tìm x, biết:
\(\frac{\left(2019-x\right)^2+\left(2019-x\right)\left(x-2020\right)+\left(x-2020\right)^2}{\left(2019-x\right)^2-\left(2019-x\right)\left(x-2020\right)+\left(x-2020\right)^2}=\frac{19}{49}\)
Các bạn mong giúp mình sớm nhé
ủa bạn j ơi chữ x chành bành ra trên đề kìa mà bạn bảo tìm làm j nữa
Cho \(f\left(x\right)=\frac{x^3}{1-3x+3x^2}.\) Tính \(A=f\left(\frac{1}{2020}\right)+f\left(\frac{2}{2020}\right)+...+f\left(\frac{2018}{2020}\right)+f\left(\frac{2019}{2020}\right).\)
Cho \(f\left(x\right)=\frac{x^3}{1-3x+3x^2}.\) Tính \(A=f\left(\frac{1}{2020}\right)+f\left(\frac{2}{2020}\right)+...+f\left(\frac{2018}{2020}\right)+f\left(\frac{2019}{2020}\right).\)
Xét \(f\left(x\right)+f\left(1-x\right)=\frac{x^3}{1-3x+3x^2}+\frac{\left(1-x\right)^3}{1-3\left(1-x\right)+3\left(1-x\right)^2}\)
\(=\frac{x^3}{1-3x+3x^2}+\frac{1-3x+3x^2-x^3}{1-3+3x+3-6x+3x^2}\)
\(=\frac{x^3}{1-3x+3x^2}+\frac{1-3x+3x^2-x^3}{1-3x+3x^2}\)
\(=\frac{1-3x+3x^2}{1-3x+3x^2}=1\)
Thay vào ta tính được:
\(A=\left[f\left(\frac{1}{2020}\right)+f\left(\frac{2019}{2020}\right)\right]+...+\left[f\left(\frac{1009}{2020}\right)+f\left(\frac{1011}{2020}\right)\right]+f\left(\frac{1010}{2020}\right)\)
\(A=1+...+1+f\left(\frac{1010}{2020}\right)\) (với 1009 số 1)
\(A=1009+f\left(\frac{1}{2}\right)=1009+\frac{\left(\frac{1}{2}\right)^3}{1-3\cdot\frac{1}{2}+3\cdot\left(\frac{1}{2}\right)^2}\)
\(A=1009+\frac{1}{2}=\frac{2019}{2}\)
Vậy \(A=\frac{2019}{2}\)
hello ae xin chào
a,Cho \(\left(x-2019+\sqrt{\left(x-2019\right)^2+2020}\right)\left(y-2019+\sqrt{\left(y-2019\right)^2+2020}\right)=2020\)Tính : D = x + y
b, Cho \(\frac{-3}{2}\le x\le\frac{3}{2},x\ne0,a=\sqrt{3+2x}-\sqrt{3-2x}\)
Tính : \(G=\frac{\sqrt{6+2\sqrt{9-4x^2}}}{x}\) theo a.
Em cảm ơn mọi người nhiều ạ.
Cho hàm số \(y=\dfrac{1}{2x^2+x-1}\). Hỏi đạo hàm cấp 2019 của hàm số bằng biểu thức nào sau đây?
A. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2^{2019}}{\left(2x-1\right)^{2020}}\right)\)
B. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2^{2020}}{\left(2x-1\right)^{2020}}\right)\)
C. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2}{\left(2x-1\right)^{2020}}\right)\)
D. \(\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}+\dfrac{2}{\left(2x-1\right)^{2020}}\right)\)
\(y=\dfrac{1}{2x^2+x-1}=\dfrac{1}{\left(x+1\right)\left(2x-1\right)}=\dfrac{2}{3}.\dfrac{1}{2x-1}-\dfrac{1}{3}.\dfrac{1}{x+1}\)
\(y'=\dfrac{2}{3}.\dfrac{-2}{\left(2x-1\right)^2}-\dfrac{1}{3}.\dfrac{-1}{\left(x+1\right)^2}=\dfrac{2}{3}.\dfrac{\left(-1\right)^1.2^1.1!}{\left(2x-1\right)^2}-\dfrac{1}{3}.\dfrac{\left(-1\right)^1.1!}{\left(x+1\right)^2}\)
\(y''=\dfrac{2}{3}.\dfrac{\left(-1\right)^2.2^2.2!}{\left(2x-1\right)^3}-\dfrac{1}{3}.\dfrac{\left(-1\right)^2.2!}{\left(x+1\right)^3}\)
\(\Rightarrow y^{\left(n\right)}=\dfrac{2}{3}.\dfrac{\left(-1\right)^n.2^n.n!}{\left(2x-1\right)^{n+1}}-\dfrac{1}{3}.\dfrac{\left(-1\right)^n.n!}{\left(x+1\right)^{n+1}}\)
\(\Rightarrow y^{\left(2019\right)}=\dfrac{2}{3}.\dfrac{\left(-1\right)^{2019}.2^{2019}.2019!}{\left(2x-1\right)^{2020}}-\dfrac{1}{3}.\dfrac{\left(-1\right)^{2019}.2019!}{\left(x+1\right)^{2020}}\)
\(=\dfrac{2019!}{3}\left(\dfrac{1}{\left(x+1\right)^{2020}}-\dfrac{2^{2020}}{\left(2x-1\right)^{2020}}\right)\)
Cho hàm số \(y=\dfrac{1}{3x^2-x-2}\). Hỏi đạo hàm cấp 2019 của hàm số bằng biểu thức nào sau đây?
A. \(\dfrac{2019!}{5}\left(\dfrac{1}{\left(x-1\right)^{2020}}-\dfrac{3}{\left(3x+2\right)^{2020}}\right)\)
B. \(\dfrac{2019!}{5}\left(\dfrac{3^{2020}}{\left(3x+2\right)^{2020}}-\dfrac{1}{\left(x-1\right)^{2020}}\right)\)
C. \(\dfrac{2019!}{5}\left(\dfrac{3}{\left(3x+2\right)^{2020}}-\dfrac{1}{\left(x-1\right)^{2020}}\right)\)
D. \(\dfrac{2019!}{5}\left(\dfrac{1}{\left(x-1\right)^{2020}}-\dfrac{3^{2020}}{\left(3x+2\right)^{2020}}\right)\)
\(y=\dfrac{1}{3x^2-x-2}=\dfrac{1}{\left(x-1\right)\left(3x+2\right)}=\dfrac{1}{5}.\dfrac{1}{x-1}-\dfrac{3}{5}.\dfrac{1}{3x+2}\)
\(y'=\dfrac{1}{5}.\dfrac{\left(-1\right)^1.1!}{\left(x-1\right)^2}-\dfrac{3}{5}.\dfrac{\left(-1\right)^1.3^1.1!}{\left(3x+2\right)^2}\)
\(y''=\dfrac{1}{5}.\dfrac{\left(-1\right)^2.2!}{\left(x-1\right)^3}-\dfrac{3}{5}.\dfrac{\left(-1\right)^2.3^2.2!}{\left(3x+2\right)^3}\)
\(\Rightarrow y^{\left(n\right)}=\dfrac{1}{5}.\dfrac{\left(-1\right)^n.n!}{\left(x-1\right)^{n+1}}-\dfrac{3}{5}.\dfrac{\left(-1\right)^n.3^n.n!}{\left(3x+2\right)^{n+1}}\)
\(\Rightarrow y^{\left(2019\right)}=\dfrac{1}{5}.\dfrac{\left(-1\right)^{2019}.2019!}{\left(x-1\right)^{2020}}-\dfrac{3}{5}.\dfrac{\left(-1\right)^{2019}.3^{2019}.2019!}{\left(3x+2\right)^{2019}}\)
\(=\dfrac{2019!}{5}\left(\dfrac{3^{2020}}{\left(3x+2\right)^{2020}}-\dfrac{1}{\left(x-1\right)^{2020}}\right)\)