matanaliz

matanaliz

University

10 Qs

quiz-placeholder

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matanaliz

matanaliz

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

Created by

Lala Huseynova

Used 4+ times

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10 questions

Show all answers

1.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Найти производную функции  

 y=x3log2xy=x^3\log_2x  

 x2(3log2x+1ln2)x^2\left(3\log_2x+\frac{1}{\ln2}\right)  

 x(4log2x+1lnx)x^{ }\left(4\log_2x+\frac{1}{\ln x}\right)  

 (3log2x+xln2)\left(3\log_2x+\frac{x}{\ln2}\right)  

 x4(3log2x+2ln2)x^4\left(3\log_2x+\frac{2}{\ln2}\right)  

2.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

дана функция

 =sinxecosx,x0=π2.=\sin x\cdot e^{\cos x},x_0=\frac{\pi}{2}.  Найти производную и вычислить ее значение при  x=x0x=x_0  .

1

-1

2

0

3.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

 y=ax(a>0)y=a^x\left(a>0\right)  

Найти производную n порядка функции   

 axa^x  

 axlnaa^x\ln a  

 lnna\ln^na  

 axlnnaa^x\ln^na  

4.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

 x12+y12=a12x^{\frac{1}{2}}+y^{\frac{1}{2}}=a^{\frac{1}{2}}  

Найти производную неявной функции

 yx=yxy_x=-\sqrt{\frac{y}{x}}  

 yx=xyy_x=-\sqrt{\frac{x}{y}}  

 yx=xy_x=-\sqrt{x}  

 yx=yy_x=-\sqrt{y}  

5.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

 y=x2 в точке M(2;4)y=x^2\ в\ точке\ M\left(2;4\right)  

Написать уравнение касательной к кривой в этой точке.

 y=2x8y=2x-8  

 y=4x4y=4x-4  

 y=3x4y=3x-4  

 y=x4y=x-4  

6.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

Найти производную третьего порядка от функции  y=xy=\sqrt{x}  

 39x72\frac{3}{9}x^{-\frac{7}{2}}  

 38x52\frac{3}{8}x^{-\frac{5}{2}}  

 310x32\frac{3}{10}x^{-\frac{3}{2}}  

 x72x^{-\frac{7}{2}}  

7.

MULTIPLE SELECT QUESTION

15 mins • 1 pt

 s=1t2s=\sqrt{1-t^2}  

Найти дифференциал функции

 11t2dt\frac{1}{\sqrt{1-t^2}}dt  

 21t2dt\frac{2}{\sqrt{1-t^2}}dt  

 11t2dt-\frac{1}{\sqrt{1-t^2}}dt  

 2t1t2dt-\frac{2t}{\sqrt{1-t^2}}dt  

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