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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.
If \(y = \sec(3x)\), then the derivative \(\frac{dy}{dx}\) is equal to:
A) $3sec(3x) tan(3x)$
D) \(3sec^2(3x)\)
C) $-3csc(3x) cot(3x)$
B) $sec(3x) tan(3x)$
2.
If a, b, c form an arithmetic sequence, then the arithmetic mean b equals:
b = sqrt(a * c)
b = (a + c) / 2
b = a + c
b = 2 a c / (a + c)
3.
If y = (2x + 1) * (3x - 4), then dy/dx evaluated at x = 1 equals:
-5
7
1
12
4.
Using the Quotient Rule, the derivative of y = (x + 3) / (x - 2) for x != 2 is:
-5 / (x - 2)2
5 / (x - 2)2
1 / (x - 2)2
(2x + 1) / (x - 2)2
5.
If y = sin(3x) + cos(2x), then dy/dx at x = 0 equals:
3
1
5
-2
6.
STEM Limits Problem 5: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
1
5/2 (or 2.5)
7.
STEM Limits Problem 6: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
1
0
Undefined
8.
STEM Limits Problem 11: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
1
5/2 (or 2.5)
Undefined
9.
STEM Limits Problem 12: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
10.
STEM Limits Problem 17: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
5/2 (or 2.5)
1
11.
STEM Limits Problem 18: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
5/2 (or 2.5)
Undefined
0
12.
STEM Limits Problem 23: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
1
0
Undefined
13.
STEM Limits Problem 24: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
14.
STEM Limits Problem 29: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
Undefined
0
1
15.
STEM Limits Problem 30: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
16.
STEM Limits Problem 35: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
5/2 (or 2.5)
Undefined
0
17.
STEM Limits Problem 36: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
Undefined
1
18.
STEM Limits Problem 41: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
Undefined
0
1
19.
STEM Limits Problem 42: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
5/2 (or 2.5)
0
1
Undefined
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