Câu 1: ĐKXĐ: 2x-3>0
=>2x>3
=>\(x>\dfrac{3}{2}\)
=>\(a=\dfrac{3}{2}\)
Câu 2:
ĐKXĐ: x>1/2
\(log_{\dfrac{1}{2}}\left(2x-1\right)=0\)
=>\(2x-1=1\)
=>2x=2
=>x=1(nhận)
Câu 3:
\(y=\sqrt{x^2-2x+3}\)
=>\(y'=\dfrac{\left(x^2-2x+3\right)'}{2\sqrt{x^2-2x+3}}=\dfrac{2x-2}{2\sqrt{x^2-2x+3}}=\dfrac{x-1}{\sqrt{x^2-2x+3}}\)
=>a=1; b=-1
a*b=1*(-1)=-1
Câu 4: \(y=\sqrt{x}+x\)
=>\(y'=1+\dfrac{1}{2\sqrt{x}}=\dfrac{2\sqrt{x}+1}{2\sqrt{x}}\)
Khi x=4 thì \(y'=\dfrac{2\sqrt{4}+1}{2\sqrt{4}}=\dfrac{5}{4}\)
Câu 5:
\(\widehat{SC;\left(ABCD\right)}=\widehat{CS;CA}=\widehat{SCA}\)
ABCD là hình vuông
=>\(AC=\sqrt{AB^2+BC^2}=a\sqrt{2}\)
Xét ΔSAC vuông tại A có \(tanSCA=\dfrac{SA}{AC}=1\)
nên \(\widehat{SCA}=45^0\)
=>\(\widehat{SC;\left(ABCD\right)}=45^0\)