100+ câu trắc nghiệm Giải tích 3 có đáp án - Phần 2

A.$dy=\cos \left(sinx\right)sinxdx$

B.$dy=\sin \left(\cos x\right)dx$

C.$dy=\cos \left(sinx\right)cosxdx$

D.$dy=\cos \left(sinx\right)dx$

A.$df\left(0\right)=-dx$

B.$f^{\text{'}}\left(0^{+}\right)=\underset{x\to 0^{+}}{\lim } \frac{x^2-x}{x}=\underset{x\to 0^{+}}{\lim }(x-1)=-1$

C.$f^{\text{'}}\left(0^{+}\right)=\underset{x\to 0^{+}}{\lim }(x^2-x)=0$

D.$f^{\text{'}}\left(0^{-}\right)=\underset{x\to 0^{-}}{\lim }2x=0$

A.$dy=4\cos 2x\sin 2xdx$

B.$dy=2\cos 2x\sin 2xdx$

C.$dy=-2\cos 2x\sin 2xdx$

D.$dy=-2\sin 4xdx$

A.$f^{\text{'}}\left(0^{+}\right)=1$

B.$f^{\text{'}}\left(0^{-}\right)=1$

C.$df\left(0\right)=dx$

D. Hàm số không có vi phân tại x=0.

A.$df\left(x\right)=\frac{-\sin \left(4x\right)}{2\sqrt{1+{\cos }^{2}2x}}dx$

B.$df\left(x\right)=\frac{-\sin \left(4x\right)}{\sqrt{1+{\cos }^{2}2x}}dx$

C.$df\left(x\right)=\frac{\cos \left(2x\right)}{\sqrt{1+{\cos }^{2}2x}}dx$

D.$df\left(x\right)=\frac{-\sin \left(2x\right)}{\sqrt{1+{\cos }^{2}2x}}dx$

A.$dy=\frac{1}{2\sqrt{x}{\cos }^{2}x}dx$

B.$dy=\frac{1}{\sqrt{x}{\cos }^2\sqrt{x}}dx$

C. .$dy=\frac{1}{2\sqrt{x}\cos \sqrt{x}}dx$

D.$dy=\frac{1}{2\sqrt{x}{\cos }^2\sqrt{x}}dx$

A.$dy=\frac{-8}{{(2x-1)}^2}dx$

B.$dy=\frac{4}{{(2x-1)}^2}dx$

C.$dy=\frac{-4}{{(2x-1)}^2}dx$

D.$dy=\frac{-7}{{(2x-1)}^2}dx$

A.$dy=\frac{-4x}{{(1+x^2)}^2}dx$

B.$dy=\frac{-4}{{(1+x^2)}^2}dx$

C.$dy=\frac{-4}{1+x^2}dx$

D.$dy=\frac{-dx}{{(1+x^2)}^2}$

A.$d\left[f\left(x\right)\right]=\frac{\sin 2x}{2\sqrt{\cos 2x}}dx$

B.$d\left[f\left(x\right)\right]=\frac{\sin 2x}{\sqrt{\cos 2x}}dx$

C.$d\left[f\left(x\right)\right]=\frac{-\sin 2x}{2\sqrt{\cos 2x}}dx$

D.$d\left[f\left(x\right)\right]=\frac{-\sin 2x}{\sqrt{\cos 2x}}dx$

A. \(y'' = 0\).

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

C. \(y'' = - \frac{4}{{{{\left( {x - 2} \right)}^2}}}\).

D. \(y'' = \frac{4}{{{{\left( {x - 2} \right)}^3}}}\).

A. \[y''' = {\rm{ }}12\left( {{x^2} + {\rm{ }}1} \right)\].

B. \[y''' = {\rm{ }}24\left( {{x^2} + {\rm{ }}1} \right)\].

C. \[y''' = {\rm{ }}24\left( {5{x^2} + {\rm{ }}3} \right)\].

D. \[y''' = {\rm{ }}-12\left( {{x^2} + {\rm{ }}1} \right)\].

A. \(y'' = \frac{1}{{(2x + 5)\sqrt {2x + 5} }}\).

B. \(y'' = \frac{1}{{\sqrt {2x + 5} }}\).

C. \(y'' = - \frac{1}{{(2x + 5)\sqrt {2x + 5} }}\).

D. \(y'' = - \frac{1}{{\sqrt {2x + 5} }}\).

A. \({y^{(5)}} = - \frac{{120}}{{{{(x + 1)}^6}}}\).

B. \({y^{(5)}} = \frac{{120}}{{{{(x + 1)}^6}}}\).

C. \({y^{(5)}} = \frac{1}{{{{(x + 1)}^6}}}\).

D. \({y^{(5)}} = - \frac{1}{{{{(x + 1)}^6}}}\).

A. \[{y^{\left( 5 \right)}} = - \frac{{120}}{{{{\left( {x + 1} \right)}^6}}}\].

B. \[{y^{\left( 5 \right)}} = \frac{{120}}{{{{\left( {x + 1} \right)}^5}}}\].

C. \[{y^{\left( 5 \right)}} = \frac{1}{{{{\left( {x + 1} \right)}^5}}}\].

D. \[{y^{\left( 5 \right)}} = - \frac{1}{{{{\left( {x + 1} \right)}^5}}}\].

A. \[y'' = - \frac{{2{x^3} + 3x}}{{\left( {1 + {x^2}} \right)\sqrt {1 + {x^2}} }}\].

B. \[y'' = \frac{{2{x^2} + 1}}{{\sqrt {1 + {x^2}} }}\].

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

D. \[y'' = - \frac{{2{x^2} + 1}}{{\sqrt {1 + {x^2}} }}\].

A. \[y''' = 80{\left( {2x + 5} \right)^3}\].

B. \[y''' = 480{\left( {2x + 5} \right)^2}\].

C. \[y''' = - 480{\left( {2x + 5} \right)^2}\].

D. \[y''' = - 80{\left( {2x + 5} \right)^3}\].

A. \[y'' = - \frac{{2\sin x}}{{{{\cos }^3}x}}\].

B. \[y'' = \frac{1}{{{{\cos }^2}x}}\].

C. \[y'' = - \frac{1}{{{{\cos }^2}x}}\].

D. \[y'' = \frac{{2\sin x}}{{{{\cos }^3}x}}\].

A. \[y' = \sin \left( {x + \frac{\pi }{2}} \right)\].

B. \[y'' = \sin \left( {x + \pi } \right)\].

C. \[y''' = \sin \left( {x + \frac{{3\pi }}{2}} \right)\].

D. \[{y^{\left( 4 \right)}} = \sin \left( {2\pi - x} \right)\].

A. \[y'' = 2 + \frac{1}{{{{\left( {1 - x} \right)}^2}}}\].

B. \[y'' = \frac{2}{{{{\left( {1 - x} \right)}^3}}}\].

C. \[y'' = \frac{{ - 2}}{{{{\left( {1 - x} \right)}^3}}}\].

D. \[y'' = \frac{2}{{{{\left( {1 - x} \right)}^4}}}\].

A. \[x = \frac{\pi }{2}\].

B. \(x = 0\) và \[x = \frac{\pi }{6}\].

C. \(x = 0\) và \[x = \frac{\pi }{3}\].

D. \(x = 0\) và \[x = \frac{\pi }{2}\].

A. \[4y - y' = 0\].

B. \[4y + y'' = 0\].

C. \(y = y'tan2x\).

D. \({y^2} = {\left( {y'} \right)^2} = 4\).

A. Chỉ \[\left( I \right)\] đúng.

B. Chỉ \[\left( {II} \right)\] đúng.

C. Cả hai đều đúng.

D. Cả hai đều sai.

A. \[\frac{1}{{\cos x}}\].

B. \[ - \frac{1}{{\cos x}}\].

C. \(\cot x\).

D. \(tanx\).

A. Chỉ \[\left( I \right)\] đúng.

B. Chỉ \[\left( {II} \right)\] đúng.

C. Cả hai đều đúng.

D. Cả hai đều sai.

A. \[3\].

B. \[6\].

C. \(12\).

D. \(24\).

A. \[0\].

B. \[ - 1\].

C. \( - 2\).

D. \(5\).

A. \[\left[ { - 1;2} \right]\].

B. \[\left( { - \infty ;0} \right]\].

C. \(\left\{ { - 1} \right\}\).

D. \(\emptyset \).

A. \[y'''\left( 1 \right) = \frac{3}{8}\].

B. \[y'''\left( 1 \right) = \frac{1}{8}\].

C. \[y'''\left( 1 \right) = - \frac{3}{8}\].

D. \[y'''\left( 1 \right) = - \frac{1}{4}\].

A. \[{y^{\left( {10} \right)}}\left( 1 \right) = 0\].

B. \[{y^{\left( {10} \right)}}\left( 1 \right) = 10a + b\].

C. \[{y^{\left( {10} \right)}}\left( 1 \right) = 5a\].

D. \[{y^{\left( {10} \right)}}\left( 1 \right) = 10a\].