What is the first derivative of ln(x)?

Understanding Taylor and Maclaurin Series

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Mathematics
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10th - 12th Grade
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Hard

Emma Peterson
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
1/x
x
ln(x)
x^2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the value of the natural log of 1?
ln(1)
Undefined
0
1
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the Taylor series expansion, what does the term F'(C) represent?
The original function
The first derivative evaluated at C
The second derivative evaluated at C
The constant term
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What remains constant in the Taylor series for e^x centered at c=3?
x
e^3
The factorials
The exponents
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first derivative of sine(x)?
Negative cosine(x)
Negative sine(x)
Sine(x)
Cosine(x)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the Maclaurin series for cosine(x) using the series for sine(x)?
Add the series for sine(x) to itself
Multiply the series for sine(x) by x
Differentiate the series for sine(x)
Integrate the series for sine(x)
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the power-reducing formula for cosine squared?
1/2 * (1 + cosine(2x))
1/2 * (1 - cosine(2x))
cosine^2(x) + sine^2(x)
1 - sine^2(x)
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