125 câu trắc nghiệm tổng hợp Toán cao cấp A1 có đáp án - Phần 4

A. f'(0) = 0

B. f'(0) = -1

C. f'(0) = 1

D. Không tồn tại

A. \[{{\rm{a}}^{\rm{n}}}{\rm{.}}{{\rm{e}}^{{\rm{ax}}}}\]

B. \[{{\rm{a}}^{\rm{n}}} - 1.{{\rm{e}}^{{\rm{ax}}}}\]

C. \[{{\rm{a}}^{\rm{n}}}{\rm{.}}{{\rm{e}}^{\rm{x}}}\]

D. Kết quả khác

A. -1

B. +∞

C. 0

D. e-1/2

A. \[{\rm{y = x}} - \frac{1}{4}\]

B. \[{\rm{y = }}\frac{{\rm{x}}}{{\rm{2}}} - \frac{1}{2}\]

C. \[{\rm{y = }}\frac{{\rm{x}}}{{\rm{2}}} - \frac{1}{4}\]

D. \[{\rm{y = }}\frac{{\rm{x}}}{{\rm{2}}} + \frac{1}{4}\]

A. Đáp án khác

B. \[{{\rm{f'}}_ - }(0) = - 1\]

C. \[{{\rm{f'}}_ - }(0) = 0\]

D. \[{{\rm{f'}}_ - }(0) = 1\]

A. \[\frac{{({\rm{n}} - 1)!}}{{{{\rm{x}}^{\rm{n}}}}}\]

B. Kết quả khác

C. \[{( - 1)^{{\rm{n}} - 1}}.\frac{{({\rm{n}} - 1)!}}{{{{\rm{x}}^{\rm{n}}}}}\]

D. \[{{\rm{a}}^{{\rm{n}} - 1}}.{{\rm{e}}^{{\rm{ax}}}}\]

A. 0

B. -1/80

C. 10

D. 20

A. 2x - 3

B. 0

C. 3 - 2x

D. 2x + 3

A. 0

B. -1

C. -2

D. -1/2

A. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = - \mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

B. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = 2\mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

C. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = \mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

D. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = 0\]

A. r = 1/e

B. r = 1

C. r = e

D. \[ + \infty \]

A. \[\mathop \smallint \limits_{\rm{a}}^{\rm{c}} {\rm{f(x)dx}} + \mathop \smallint \limits_{\rm{c}}^{\rm{b}} {\rm{f(x)dx}};{\rm{c}} \in {\rm{R}}\]

B. \[\mathop \smallint \limits_{\rm{a}}^{\rm{c}} {\rm{f(x)dx}} + \mathop \smallint \limits_{\rm{c}}^{\rm{b}} {\rm{f(x)dx}};a \le c \le b\]

C. \[\mathop \smallint \limits_{\rm{c}}^{\rm{a}} {\rm{f(x)dx}} + \mathop \smallint \limits_{\rm{b}}^{\rm{c}} {\rm{f(x)dx}};a \le c \le b\]

D. \[\mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(t)dx}}\]

A. \[ - \frac{1}{4}\ln 5 + \frac{2}{3}\ln 2\]

B. \[\frac{1}{4}\ln 5 + \frac{2}{3}\ln 2\]

C. \[ - \frac{1}{4}\ln 5\]

D. \[\frac{2}{3}\ln 2\]

A. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = 2\mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

B. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = - \mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

C. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = \mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

D. \[\mathop \smallint \limits_{ - {\rm{a}}}^{\rm{a}} {\rm{f(x)dx}} = 2\mathop \smallint \limits_{ - a/2}^{{\rm{a/2}}} {\rm{f(x)dx}}\]

A. \[\frac{1}{5}\]

B. \[\frac{1}{{64}}\]

C. \[\frac{1}{8}\]

D. \(\infty \)

A. \[\frac{{\rm{1}}}{{\rm{3}}}{\rm{\pi b}}{{\rm{a}}^{\rm{2}}}\]

B. \[\frac{{\rm{2}}}{{\rm{3}}}{\rm{\pi b}}{{\rm{a}}^{\rm{2}}}\]

C. \[\frac{{\rm{4}}}{{\rm{3}}}{\rm{\pi b}}{{\rm{a}}^{\rm{2}}}\]

D. \[{\rm{\pi b}}{{\rm{a}}^{\rm{2}}}\]

A. \[{{\rm{u}}_{\rm{1}}}{\rm{ + }}{{\rm{u}}_{\rm{2}}}{\rm{ + }}...{\rm{ + }}{{\rm{u}}_{\rm{n}}}{\rm{ + }}...\]được gọi là một dãy số

B. \[\mathop \sum \limits_{{\rm{i = 1}}}^{\rm{n}} {{\rm{u}}_{\rm{i}}}\]được gọi là một chuỗi số

C. \[{{\rm{u}}_{\rm{1}}}{\rm{ + }}{{\rm{u}}_{\rm{2}}}{\rm{ + }}...{\rm{ + }}{{\rm{u}}_{\rm{n}}}{\rm{ + }}...\]được gọi là một chuỗi số

D. \[{\rm{u}}_{\rm{1}}^{\rm{2}}{\rm{, u}}_{\rm{2}}^{\rm{2}}{\rm{,}}...{\rm{u}}_{\rm{n}}^{\rm{2}}{\rm{,}}...\]được gọi là một chuỗi số dương

A. \[{\rm{S}} = + \infty \]

B. S = 2

C. S = 3

D. S = 0

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

B. -1

C. 1

D. 0

A. \[\left( {\forall {\rm{x}} \in \left[ {{\rm{a,b}}} \right]} \right){\rm{f(x)}} < {\rm{g(x)}} \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(x)dx}} > \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{g(x)dx}}\]

B. \[\left( {\forall {\rm{x}} \in \left[ {{\rm{a,b}}} \right]} \right){\rm{f(x)}} \le {\rm{g(x)}} \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(x)dx}} \le \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{g(x)dx}}\]

C. \[\left( {\forall {\rm{x}} \in \left[ {{\rm{a,b}}} \right]} \right){\rm{f(x)}} \le {\rm{g(x)}} \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{f(x)g(x)dx}} \le \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{g(x)dx}}\]

D. \[{\rm{f(x)}} \le {\rm{g(x)}} \Rightarrow \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{g(x)dx}} \le \mathop \smallint \limits_{\rm{a}}^{\rm{b}} {\rm{g(x)dx}}\]

A. \[\mathop \smallint \limits_{\rm{a}}^{{\rm{a + T}}} {\rm{f(x)dx}} = - \mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

B. \[\mathop \smallint \limits_{\rm{a}}^{{\rm{a + T}}} {\rm{f(x)dx}} = \mathop \smallint \limits_0^{\rm{a}} {\rm{f(x)dx}}\]

C. \[\mathop \smallint \limits_{\rm{a}}^{{\rm{a + T}}} {\rm{f(x)dx}} = 0\]

D. \[\mathop \smallint \limits_{\rm{a}}^{{\rm{a + T}}} {\rm{f(x)dx}} = - \mathop \smallint \limits_T^{\rm{a}} {\rm{f(x)dx}}\]

A. \[\frac{2}{3}\ln 2\]

B. \[\frac{3}{2}\ln 2\]

C. \[ - \frac{2}{3}\ln 2\]

D. \[{\rm{ln2}}\]

A. 0

B. \[\ln \frac{{\sqrt 2 + 1}}{{\sqrt 2 - 1}}\]

C. \[\ln \frac{{\sqrt 2 + 1}}{3}\]

D. \[\ln \frac{{\sqrt 2 + 1}}{{3(\sqrt 2 - 1)}}\]

A. \[\frac{1}{5}\]

B. 0

C. \(\infty \)

D. \[\frac{1}{{10}}\]

A. \[1 + {\rm{ln2}}\]

B. \[1 - {\rm{ln2}}\]

C. \[\frac{1}{5}\ln 2\]

D. \[\frac{{12}}{5}\ln 6\]