Trắc nghiệm Hàm số mũ. Hàm số lôgarit Toán Lớp 12

A. \(\begin{array}{ll} m \in(-\infty ;-4) \cup(1 ;+\infty) . \end{array}\)

B. \( m \in(1 ;+\infty) . \)

C. \(m \in(-4 ; 1) .\)

D. \(m \in(1 ;+\infty) .\)

A. \(\left[\begin{array}{l}m<-2 \\ m>2\end{array}\right.\)

B. \(m\le 2\)

C. -2<m<2

D. \(m\ge2\)

A. \(m \leq 3\)

B. \(m \geq -3\)

C. m<0

D. m>1

A. \(D=(2 ; 3) .\)

B. \(D=(-3 ; 3) \backslash\{2\} .\)

C. \(D=(3 ;+\infty) . \)

D. \(D=(-3 ; 3)\)

A. \(\mathrm{D}=\left[-2 ; \frac{3}{2}\right) \cup\left(\frac{3}{2} ; 2\right] .\)

B. \(\mathrm{D}=\left(-2 ; \frac{3}{2}\right) \cup\left(\frac{3}{2} ; 2\right)\)

C. \(\mathrm{D}=\left(\frac{3}{2} ; 2\right) .\)

D. \(\mathrm{D}=(-2 ; 2)\)

A. \(\mathbb{R}\)

B. \((3 ;+\infty)\)

C. \((0 ;+\infty)\)

D. \((2 ;+\infty)\)

A. \([0 ;+\infty) .\)

B. \((-\infty ; 3) \text { . }\)

C. \([0 ; 3)\)

D. \((0 ; 3)\)

A. \(D=(-\infty ; 2] \cup[3 ;+\infty)\)

B. D=(-3 ; 1)

C. \(D=\mathbb{R}\)

D. \(D=[3 ;+\infty)\)

A. \((6 ;+\infty)\)

B. \((0 ;+\infty)\)

C. \(\mathbb{R}\)

D. \((-\infty ; 6)\)

A. \((-\infty ; 2] \cup[3 ;+\infty)\)

B. (2 ; 3)

C. \((-\infty ; 2) \cup(3 ;+\infty)\)

D. [2 ; 3]

A. \(D=\mathbb{R}\)

B. \( D=(0 ;+\infty)\)

C. \(D=(-\infty ; 0) \cup(3 ;+\infty)\)

D. \(D=(0 ; 3)\)

A. \(D=(-\infty ;-2)\)

B. \(D=(2 ;+\infty)\)

C. \(D=(-2;3)\)

D. \(D=(-\infty ;-1) \cup(3 ;+\infty)\)

A. \(D=(-\infty ;-3) \)

B. \(D=(-\infty ;-2) \cup(3 ;+\infty) \text { . }\)

C. \(D=(3 ;+\infty) \text { . }\)

D. \(D=(-\infty ;-3) \cup(3 ;+\infty) \text { . }\)

A. \(g^{\prime}(x)=\frac{1}{x} .\)

B. \(g^{\prime}(x)=\frac{1}{x \ln 3} . \)

C. \( g^{\prime}(x)=\frac{\ln 3}{x} . \)

D. \(g^{\prime}(x)=\frac{x}{\ln 3} .\)

A. \(\begin{array}{ll} \log _{a} f(x)=g(x) \Leftrightarrow f(x)=a^{g(x)} \end{array}\)

B. \(a^{f(x)}=b \Leftrightarrow f(x)=\log _{a} b \)

C. \(a^{f(x)} b^{g(x)}=c \Leftrightarrow f(x)+g(x) \log _{a} b=\log _{a} c \)

D. \( \log _{a} f(x)<g(x) \Leftrightarrow 0<f(x)<a^{g(x)}\)

A. \(\begin{array}{l} y^{\prime}=\frac{-2 \cos x}{2 \sin x-1} . \end{array}\)

B. \( y^{\prime}=\frac{2 \cos x}{2 \sin x-1} \text { . }\)

C. \(y^{\prime}=\frac{2 \cos x}{(2 \sin x-1) \ln 10} . \)

D. \( y^{\prime}=\frac{-2 \cos x}{(2 \sin x-1) \ln 10} .\)

A. \(y^{\prime}=\frac{1}{\left(x^{2}-x\right) \ln 10}\)

B. \(y^{\prime}=\frac{2 x-1}{x^{2}-x} \)

C. \(y^{\prime}=\frac{2 x-1}{\left(x^{2}-x\right) \log e}\)

D. \(y^{\prime}=\frac{2 x-1}{x^{2}-x} \cdot \log e\)

A. \(y^{\prime}=\frac{1}{2 \sqrt{x^{2}+1}} \cdot\)

B. \(y^{\prime}=\frac{2 x}{x+\sqrt{x^{2}+1}} \cdot \)

C. \(y^{\prime}=\frac{1}{x+\sqrt{x^{2}+1}} \cdot\)

D. \( y^{\prime}=\frac{1}{\sqrt{x^{2}+1}} .\)

A. \(\begin{array}{llll} \frac{1}{3} . \end{array}\)

B. \( \frac{1}{3 \ln 3}+2 .\)

C. \( \frac{1}{3 \ln 3}-1 .\)

D. \(\frac{1}{3 \ln 3} .\)

A. \(\frac{\ln 2}{2}\)

B. 1

C. 2

D. \(\frac{1}{2}\)

A. \(\begin{array}{l} y^{\prime}=\frac{2 x+1}{\left(x^{2}+x+1\right) \ln 5} \end{array}\)

B. \(y^{\prime}=\frac{2 x+1}{x^{2}+x+1} \text { . }\)

C. \(y^{\prime}=(2 x+1) \ln 5 . \)

D. \( y^{\prime}=\frac{1}{\left(x^{2}+x+1\right) \ln 5} .\)

A. \(f^{\prime}(3)=-1,5 . \)

B. \( f^{\prime}(2)=0 .\)

C. \( f^{\prime}(5)=1,2 .\)

D. \(f^{\prime}(-1)=-1,2 .\)

A. \(\begin{array}{ll} y^{\prime}=\frac{2}{x \ln 2 x \cdot \ln 10} \cdot \end{array}\)

B. \( y^{\prime}=\frac{1}{x \ln 2 x \cdot \ln 10} . \)

C. \(y^{\prime}=\frac{1}{2 x \ln 2 x \cdot \ln 10} \)

D. \(y^{\prime}=\frac{1}{x \ln 2 x}\)

A. \(y^{\prime}=\frac{1}{(4 x+1) \ln 3} . \)

B. \(y^{\prime}=\frac{4}{(4 x+1) \ln 3} .\)

C. \(y^{\prime}=\frac{\ln 3}{4 x+1}\)

D. \(y^{\prime}=\frac{4 \ln 3}{4 x+1}\)

A. \(y^{\prime}=\frac{1}{2 \sqrt{x+1}(1+\sqrt{x+1})}\)

B. \(y^{\prime}=\frac{1}{1+\sqrt{x+1}}\)

C. \(y^{\prime}=\frac{1}{\sqrt{x+1}(1+\sqrt{x+1})}\)

D. \(y^{\prime}=\frac{2}{\sqrt{x+1}(1+\sqrt{x+1})}\)

A. \(y^{\prime}=\frac{1-2 x}{\left(x^{2}-x+1\right) \ln 2} \cdot\)

B. \(y^{\prime}=\frac{2 x-1}{\left(x^{2}-x+1\right) \ln 2}\)

C. \(y^{\prime}=\frac{2-x}{\left(x^{2}-x+1\right) \ln 2}\)

D. \( y^{\prime}=\frac{2+x}{\left(x^{2}-x+1\right) \ln 2}\)

A. \(\begin{array}{l} y=\log _{2} x \text { . } \end{array}\)

B. \(y=x^{2}+\log _{2} x . \)

C. \(y=x+\log _{2} x . \)

D. \( y=\log _{2} \frac{1}{x} \text { . }\)

A. \(m \in(-\infty ;-4) \cup(1 ;+\infty) .\)

B. \(m \in[1 ;+\infty) . \)

C. \( m \in(-4 ; 1) .\)

D. \(m \in(1 ;+\infty) .\)

A. 0

B. 1

C. 2

D. 3

A. \(\left(-\frac{1}{3} ;+\infty\right) .\)

B. \(\left[-\frac{1}{3} ;+\infty\right) .\)

C. \( \mathbb{R}\)

D. \(\mathbb{R} \backslash\left\{-\frac{1}{3}\right\} .\)

A. \(\begin{array}{ll} D=(-\infty ; 1) \cup(5 ;+\infty) . \end{array}\)

B. \( D=(1 ; 5) . \)

C. \(D=(-\infty ; 1] \cup[5 ;+\infty) .\)

D. \(D=[1 ; 5] .\)

A. \(m>\frac{1}{4}\)

B. \(m>0\)

C. \(m \geq \frac{1}{4}\)

D. \(m<\frac{1}{4}\)

A. \(\left(\begin{array}{llll} 1 ;+\infty) . \end{array}\right.\)

B. \((-\infty ; \sqrt{2}) . \)

C. \( \varnothing .\)

D. \([\sqrt{2} ;+\infty) .\)

A. \(\left[\begin{array}{llll} 1 ;+\infty) \end{array}\right.\)

B. \((1 ;+\infty) . \)

C. \((2 ;+\infty) . \)

D. \([2 ;+\infty) .\)

A. \(\begin{array}{l} (-8 ;-4) \cup(3 ;+\infty) \end{array}\)

B. \((-\infty ;-4) \cup(3 ;+\infty) . \)

C. \((-8 ; 3) \backslash\{-4\} .\)

D. \((-4 ; 3) \text { . }\)

A. 1

B. 2

C. 3

D. 4

A. \(\frac{1}{4}\)

B. 1

C. 2

D. \(\frac{1}{2}\)

A. \(\begin{array}{llll} e+\frac{1}{e} . \end{array}\)

B. \(e-\frac{1}{e} . \)

C. \(-e+\frac{1}{e} .\)

D. \(-e-\frac{1}{e} .\)

A. \(y^{\prime}=3^{6 x+2} \cdot 2\)

B. \(y^{\prime}=(6 x+1) \cdot 3^{6 x} .\)

C. \(y^{\prime}=3^{6 x+2} .2 \ln 3\)

D. \(y^{\prime}=3^{6 x+1} \cdot \ln 3\)

A. \(y=\left(\frac{\pi}{3+\sqrt{5}}\right)^{x} . \)

B. \( y=\left(\frac{2}{e}\right)^{x} .\)

C. \( y=\left(\frac{3}{\sqrt{3}+\sqrt{2}}\right)^{x} . \)

D. \(y=3^{-x}\left(\frac{1}{\sqrt{3}-\sqrt{2}}\right)^{x} .\)

A. \(y=\left(\frac{\pi}{4}\right)^{x} . \)

B. \( y=\left(\frac{2}{e}\right)^{x} \cdot\)

C. \(y=\left(\frac{2}{\sqrt{3}+1}\right)^{x} .\)

D. \(y=\left(\frac{e+1}{\pi}\right)^{x} .\)

A. \(\begin{array}{l} a \in\left(-\infty ; \frac{1}{3}\right) . \end{array}\)

B. \(a \in(-3 ;+\infty) . \)

C. \( a \in\left(-\infty ; \frac{1}{3}\right] .\)

D. \( a \in\left(\frac{1}{3} ; 3\right) \text { . }\)

A. \(\begin{array}{ll} x y^{\prime \prime}-2 y^{\prime}+x y=-2 \sin x \end{array}\)

B. \(x y^{\prime}+y y^{\prime \prime}+2x y^{\prime}=2 \sin x\)

C. \(x y^{\prime}+y y^{\prime}-x y^{\prime}=2 \sin x \)

D. \(x y^{\prime \prime}+y^{\prime}-x y=2 \cos x+\sin x\)

A. \(y^{\prime}=\frac{3 e^{2 x}}{\left(e^{2 x}+1\right)^{2}}\)

B. \( y^{\prime}=\frac{e^{2 x}}{\left(e^{2 x}+1\right)^{2}}\)

C. \( y^{\prime}=\frac{2 e^{2 x}}{\left(e^{2 x}+1\right)^{2}} \)

D. \(y^{\prime}=\frac{4 e^{2 x}}{\left(e^{2 x}+1\right)^{2}}\)

A. \(x y^{\prime}+1=-e^{y} \)

B. \(x y^{\prime}-1=-e^{y}\)

C. \( x y^{\prime}-1=e^{y}\)

D. \(x y^{\prime}+1=e^{y}\)

A. \(1 \leq m \leq 2\)

B. \( 1<m \leq 2\)

C. \(-1<m<2\)

D. \(-1 \leq m \leq 2\)

A. Hàm số có một điểm cực đại.

B. Hàm số có một điểm cực tiểu.

C. Hàm số không có cực trị

D. Hàm số có một điểm cực đại và một điểm cực tiểu

A. \(\begin{array}{l} \max y=4 ; \min y=-\frac{1}{4} \end{array}\)

B. \(\max y=4 ; \text { miny }=\frac{1}{4}\)

C. \(\max y=1 ; \text { miny }=\frac{1}{4}\)

D. \( \max y=4 ; \min y=1\)

A.  

B.  

C.  

D.

A. e

B. \(\frac{1}{e}\)

C. 2e

D. 0