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Mathematics

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Unit 3

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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 \(f(x) = 5^{x^2}\) with respect to \(x\) is:
A) \(2x cdot 5^{x^2}\)
B) \(2x cdot 5^{x^2} cdot ln 5\)
C) \(5^{x^2} / ln 5\)
D) \(x^2 cdot 5^{x^2 - 1}\)
2.
The common ratio r of the geometric sequence (64, 32, 16, 8, ...) is:
r = -1/2
r = 4
r = 1/2
r = 2
3.
If f(x) = |x - 3|, the derivative f'(3) at x = 3:
Does not exist because the left-hand derivative (-1) does not equal the right-hand derivative (+1)
Equals 1
Equals -1
Equals 0
4.
The slope of the tangent to the curve y = (x + 1)/(x - 1) at x = 2 is:
2
-1
3
-2
5.
STEM Limits Problem 2: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
5/2 (or 2.5)
1
6.
STEM Limits Problem 3: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
Undefined
5/2 (or 2.5)
1
0
7.
STEM Limits Problem 8: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
5/2 (or 2.5)
0
8.
STEM Limits Problem 9: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
9.
STEM Limits Problem 14: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
10.
STEM Limits Problem 15: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
11.
STEM Limits Problem 20: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
Undefined
5/2 (or 2.5)
1
12.
STEM Limits Problem 21: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
5/2 (or 2.5)
Undefined
0
13.
STEM Limits Problem 26: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
Undefined
5/2 (or 2.5)
1
0
14.
STEM Limits Problem 27: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
0
Undefined
5/2 (or 2.5)
15.
STEM Limits Problem 32: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
0
1
5/2 (or 2.5)
Undefined
16.
STEM Limits Problem 33: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
17.
STEM Limits Problem 38: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
Undefined
0
5/2 (or 2.5)
18.
STEM Limits Problem 39: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
5/2 (or 2.5)
Undefined
0
19.
STEM Limits Problem 44: Evaluate the limit: lim [x -> 0] (sin(5x) / tan(2x)).
1
5/2 (or 2.5)
Undefined
0
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