MAT112 Calculus 2 Professor Porter Sample Test #4 Taylor ...
MAT152 Calculus 2 Professor Porter Test #3 Taylor Series NAME:_________________________________
1. Describe roughly in words how a calculator computes values for a function like sine.
2. Use the first three terms of the Maclaurin series for f(x) = sin (x) to approximate sin (.2)
ANSWER:_______________
3. Find the T3 terms of the Taylor Series for the sin(x) function centered around a = π/4
ANSWER:_______________
Why would we prefer the Taylor series centered around π/4 to the Maclaurin series?
4. Find the integral [pic]to about 4 decimal places by using three terms in the Maclaurin series.
ANSWER:_______________
What does the calculator say the integral is?
ANSWER:_______________
5. Find the first 3 terms of the Maclaurin Series for the function [pic]and give in sigma notation.
ANSWER:_______________
What is the interval of convergence for this function?
How do we know if the following series converges?
6. [pic]
-Identify the test:________________________
-Verify that the criteria were met.
-How does the series converge? Absolutely? Conditionally? Diverge?
7. [pic]
-Identify the test:________________________
-Verify that the criteria were met.
-How does the series converge? Absolutely? Conditionally? Diverge?
8. [pic]
-Identify the test:________________________
-Verify that the criteria were met.
-Does the series converge or diverge?
.
9. [pic]
-Identify the test:________________________
-Verify that the criteria were met.
-Does the series converge or diverge?
10. [pic]
-Identify the test:________________________
-Verify that the criteria were met.
-Does the series converge or diverge?
ANSWER:_______________
11. If a $1000 box depreciates at the end of every tax year by 5% of its value at the end of the year, how much will it be worth after 20 years?
ANSWER:_______________
What is the sum total of the amounts that the box was worth every year?
ANSWER:_______________
12. Find the general term of the sequence starting with n=0, determine if the sequence converges to zero.
[pic]
ANSWER:_______________
Is the sequence monotone decreasing? Why?
ANSWER:_______________
What is the difference between a series and a sequence?
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