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Mathematics

Unit 1

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Unit 2

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Unit 3

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Unit 4

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Unit 5

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Unit 6

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Unit 7

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Quiz

Lesson 1 Quiz: Complex Numbers in Trigonometric and Exponential Form and De Moivres Theorem

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  • Questions count: 19
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1.
The derivative of f(x) = 4 x3 - 5 x2 + 7 x - 9 with respect to x is:
f'(x) = 12 x3 - 10 x2 + 7
f'(x) = 12 x2 - 10 x + 7
f'(x) = 12 x2 - 10 x
f'(x) = 4 x2 - 5 x + 7
2.
The derivative of y = sin(3x) with respect to x is:
cos(3x)
3 sin(3x)
-3 cos(3x)
3 cos(3x)
3.
The integral \(\int \frac{2x}{x^2 + 1}\, dx\) evaluates to:
C) $2arctan x + C$
B) \(frac{1}{x^2 + 1} + C\)
A) \(ln(x^2 + 1) + C\)
D) \((x^2 + 1)^2 + C\)
4.
What is the rigorous mathematical principle for: Binomial Theorem for Positive Integer Exponent n?
The expansion has exactly n terms
The expansion of (a + b)n contains exactly (n + 1) terms, with general term T_(r+1) = nCr * an − r * br
The coefficients nCr always decrease monotonically from start to finish
The sum of coefficients in (a + b)n is equal to n2
5.
STEM Limits Problem 1: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
1
0
Undefined
6.
STEM Limits Problem 4: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
7.
STEM Limits Problem 7: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
8.
STEM Limits Problem 10: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
9.
STEM Limits Problem 13: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
5/2 (or 2.5)
0
10.
STEM Limits Problem 16: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
1
5/2 (or 2.5)
Undefined
11.
STEM Limits Problem 19: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
12.
STEM Limits Problem 22: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
1
5/2 (or 2.5)
13.
STEM Limits Problem 25: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
5/2 (or 2.5)
1
14.
STEM Limits Problem 28: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
1
Undefined
15.
STEM Limits Problem 31: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
5/2 (or 2.5)
0
16.
STEM Limits Problem 34: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
5/2 (or 2.5)
0
17.
STEM Limits Problem 37: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
1
5/2 (or 2.5)
Undefined
18.
STEM Limits Problem 40: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
5/2 (or 2.5)
0
19.
STEM Limits Problem 43: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
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