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ТФКП 3 семестр ЗО

Authored by Oxana Sheremet

Mathematics

University

Used 1+ times

ТФКП 3 семестр ЗО
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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Запишите значение функции в алгебраической форме

Ln (−ei)\text{Ln}\ \left(-ei\right)

1−iπ2+2iπk1-\frac{i\pi}{2}+2i\pi k

11

1−iπ21-\frac{i\pi}{2}

1+iπ21+\frac{i\pi}{2}

i−π2+2πki-\frac{\pi}{2}+2\pi k

2.

FILL IN THE BLANKS QUESTION

5 mins • 1 pt

Найдите значение (1−i)2\left(1-i\right)^2

(a)  

3.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Найдите значение производной функции f(z)=sin⁡zzf\left(z\right)=\frac{\sin z}{z} в точке z0=πz_0=\pi

−1π-\frac{1}{\pi}

−1π2-\frac{1}{\pi^2}

00

1π\frac{1}{\pi}

1π2\frac{1}{\pi^2}

4.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Вычислите интеграл ∫ABzdz\int_{AB}zdz по отрезку прямой x=0x=0 от точки A(1;0)A\left(1;0\right) до точки B(0;2)B\left(0;2\right)

-2,5

-2

0

3

1

5.

MULTIPLE SELECT QUESTION

5 mins • 2 pts

Вычислите интеграл ∫∣z∣=3e2zdzz−i\int_{\left|z\right|=3}\frac{e^{2z}dz}{z-i}

−2πsin⁡2-2\pi\sin2

2πi⋅e2i2\pi i\cdot e^{2i}

2πi sin⁡22\pi i\ \sin2

2πi⋅e22\pi i\cdot e^2

−2πi⋅e2i-2\pi i\cdot e^{2i}

6.

FILL IN THE BLANKS QUESTION

5 mins • 1 pt

Укажите характер особой точки z=2iz=2i функции f(z)=ez−2(z2+4)2f\left(z\right)=\frac{e^z-2}{\left(z^2+4\right)^2}

(a)  

7.

MULTIPLE CHOICE QUESTION

5 mins • 2 pts

Найдите вычет функции f(z)=zsin⁡πzf\left(z\right)=\frac{z}{\sin\pi z} в точке z=0z=0

1π\frac{1}{\pi}

−1π-\frac{1}{\pi}

π\pi

−π-\pi

00

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