24.
\(\lim\limits_{x\rightarrow1}f\left(x\right)=\lim\limits_{x\rightarrow1}\dfrac{\sqrt{x}-1}{x-1}=\lim\limits_{x\rightarrow1}\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\)
\(=\lim\limits_{x\rightarrow1}\dfrac{1}{\sqrt{x}+1}=\dfrac{1}{1+1}=\dfrac{1}{2}\)
Hàm liên tục tại \(x=1\) khi:
\(\lim\limits_{x\rightarrow1}f\left(x\right)=f\left(1\right)\Rightarrow\dfrac{1}{2}=k+1\)
\(\Rightarrow k=-\dfrac{1}{2}\)
25.
\(S=\dfrac{u_1}{1-q}=\dfrac{1}{1-\left(-\dfrac{1}{2}\right)}=\dfrac{2}{3}\)
26.
\(\overrightarrow{AD}=\overrightarrow{B'C'}\) nên \(\overrightarrow{AD}\) cùng hướng với \(\overrightarrow{B'C'}\)
27.
\(cos\left(\overrightarrow{a};\overrightarrow{b}\right)=\dfrac{\overrightarrow{a}.\overrightarrow{b}}{\left|\overrightarrow{a}\right|.\left|\overrightarrow{b}\right|}\)
\(\Rightarrow\overrightarrow{a}.\overrightarrow{b}=\left|\overrightarrow{a}\right|.\left|\overrightarrow{b}\right|.cos\left(\overrightarrow{a};\overrightarrow{b}\right)=3.5.cos120^0=-\dfrac{15}{2}\)
28.
Cả 4 khẳng định này đều sai
Khẳng định đúng: \(\overrightarrow{OA}+\overrightarrow{OC'}=\overrightarrow{0}\)
29.
\(\overrightarrow{MD}+\overrightarrow{MC}=\overrightarrow{0}\) là khẳng định đúng