220 câu trắc nghiệm tổng hợp Toán cao cấp A2 có đáp án - Phần 11

A. \[{\rm{dz = (cosx + siny + x + y)dy}}\]

B. \[{\rm{dz = (cosx + y)dx + (x}} - {\rm{siny)dy}}\]

C. \[{\rm{dz = (cosx + siny + x + y)dx}}\]

D. \[{\rm{dz = (cosx + y)dx + (x + siny)dy}}\]

A. 3

B. 2

C. 6

D. 9.ln3

A. M = 9, m = 2

B. M = 8, m =

C. M = 10, m = 2

D. M = 12, m = -2

A. z đạt CĐ tại\[{\rm{M}}\left( {\frac{1}{2},\frac{1}{2}} \right)\]

B. z đạt CTiểu tại B. z đạt CTiểu tại

C. z ko có cực trị

D. Các khẳng định trên sai

A. x = 1, y = 1

B. x = 0, y = 0

C. x = 1, y = 0

D. x = 0, y = 1

A. M = 8

B. M = 9

C. M = 10

D. M = 7

A. GTLN =3

B. GTLN =2

C. GTLN =1

D. GTLN = 4

A. \[z'x = 1,{\rm{ }}z'y = \frac{1}{2}\]

B. \[z'x = 0,{\rm{ }}z'y = 1\]

C. \[\;z'x = 0,{\rm{ }}z'y = - 1\]

D. \[z'x = \frac{1}{2},z'y = 1\]

A. \(\left\{ {\begin{array}{*{20}{c}}{0 \le \varphi \le \frac{{3\pi }}{4},}\\{0 \le r \le 2}\end{array}} \right.\)

B. \(\left\{ {\begin{array}{*{20}{c}}{ - \frac{\pi }{4} \le \varphi \le \frac{{3\pi }}{4},}\\{0 \le r \le 2}\end{array}} \right.\)

C. \(\left\{ {\begin{array}{*{20}{c}}{0 \le \varphi \le \pi ,}\\{0 \le r \le 2}\end{array}} \right.\)

D. \(\left\{ {\begin{array}{*{20}{c}}{0 \le \varphi \le \frac{{3\pi }}{4},}\\{0 \le r \le 4}\end{array}} \right.\)

A. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{1}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

B. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{{ - 1}}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

C. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{{2x}}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

D. \[\frac{{\partial {\rm{z}}}}{{\partial {\rm{x}}}} = \frac{x}{{\sqrt {{{\rm{x}}^{\rm{2}}}{\rm{ + }}{{\rm{y}}^{\rm{2}}}} }}\]

A. I = 3

B. \[{\rm{I}} = \frac{2}{3}\]

C. I = 1

D. I = 0

A. \[{\rm{y = }}{{\rm{e}}^{\frac{{\rm{\pi }}}{{\rm{4}}} - {\rm{arctanx}}}}\]

B. \[{\rm{y = x}}{{\rm{e}}^{\frac{{\rm{\pi }}}{{\rm{4}}} - {\rm{arctanx}}}}\]

C. \[{\rm{y = }}{{\rm{e}}^{\frac{{\rm{\pi }}}{{\rm{4}}} - x{\rm{arctanx}}}}\]

D. \[{\rm{y = }}{{\rm{e}}^{ - {\rm{arctanx}}}}\]

A. \[\frac{{32{\rm{\pi }}}}{5}\]

B. \[\frac{{64{\rm{\pi }}}}{5}\]

C. \(8\pi \)

A. \[{\rm{x}} - {\rm{y + xcosy = C}}\]

B. \[{\rm{xy}} - {\rm{xcosy = C}}\]

C. \[{\rm{xy + xcosy = C}}\]

D. \[{\rm{y}} - {\rm{x + xcosy = C}}\]

A. \[{\rm{y = C}}\left( {\rm{x}} \right){\rm{sinx}}\]

B. \[{\rm{y = }}\frac{{{\rm{C(x)}}}}{{{\rm{sinx}}}}\]

C. \[{\rm{y = C(x) + sinx}}\]

D. \[{\rm{y = C(x)}} - {\rm{sinx}}\]

A. \[\sqrt {1 + {{\rm{x}}^2}} + \ln |\ln {\rm{y}}| = {\rm{C}}\]

B. \[{\rm{arctanx + ln|lny| = C}}\]

C. $\sqrt{{\text{1+ x}}^{\text{2}}}\text{+ ylny = Carcsinx + ln|lny| = C}$

A. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{ - {\rm{x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{3x}}}}\]

B. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{\rm{x}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{3x}}}}\]

C. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{ - {\rm{x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{ - {\rm{3x}}}}\]

D. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{{\rm{2x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{3x}}}}\]

A. \[{{\rm{y}}_{\rm{r}}}{\rm{ = a}}{{\rm{e}}^{\rm{x}}}{\rm{ + b}}{{\rm{e}}^{{\rm{2x}}}}\]

B. \[{{\rm{y}}_{\rm{r}}}{\rm{ = (a}}{{\rm{x}}^{\rm{2}}}{\rm{ + bx + c)}}{{\rm{e}}^{\rm{x}}}\]

C. \[{{\rm{y}}_{\rm{r}}}{\rm{ = ax + bx + c}}\]

D. \[{{\rm{y}}_{\rm{r}}}{\rm{ = (a}}{{\rm{x}}^{\rm{2}}}{\rm{ + bx + c)}}{{\rm{e}}^{{\rm{2x}}}}\]

A. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{{\rm{2x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{\rm{x}}{{\rm{e}}^{{\rm{2x}}}}{\rm{; }}{{\rm{C}}_{\rm{1}}}{\rm{,}}{{\rm{C}}_{\rm{2}}} \in {\rm{R}}\]

B. \[{\rm{y = }}{{\rm{e}}^{{\rm{2x}}}}{\rm{ + (}}{{\rm{C}}_{\rm{1}}}{\rm{cos(2x) + }}{{\rm{C}}_{\rm{2}}}{\rm{sin(2x)); }}{{\rm{C}}_{\rm{1}}}{\rm{, }}{{\rm{C}}_{\rm{2}}} \in {\rm{R}}\]

C. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{{\rm{2x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{{\rm{e}}^{{\rm{2x}}}}{\rm{; }}{{\rm{C}}_{\rm{1}}}{\rm{,}}{{\rm{C}}_{\rm{2}}} \in {\rm{R}}\]

D. \[{\rm{y = }}{{\rm{C}}_{\rm{1}}}{{\rm{e}}^{ - {\rm{2x}}}}{\rm{ + }}{{\rm{C}}_{\rm{2}}}{\rm{x}}{{\rm{e}}^{ - {\rm{2x}}}}{\rm{; }}{{\rm{C}}_{\rm{1}}}{\rm{, }}{{\rm{C}}_{\rm{2}}} \in {\rm{R}}\]

A. I = 1

B. I = 2/3

C. I = 1

D. I = 0