# MATH 193 University of California Irvine Ratio & Convergent Geometric Final Exam

Description

will take place on 5/20/2021 (Thursday).#2. There will be 6 pages.#3. 40% of course grade#4. will be AVAILABLE at 5:00 PM and DUE by 10:00 PM.

MATH 193 (8792)
FINAL EXAM STUDY GUIDE
5-15-2021(SAT)
STUDY ALL THE NOTES, HOMEWORK PROBLEMS, & QUIZZES!
1.
THE USUAL!
2.
Series (Converge/Diverge)
(nth-Term Test for Divergence, Geometric Series Test, p-Series Test, Absolute Convergence, Alternating
Series Test, Integral Test, Direct Comparison Test, Limit Comparison Test, Ratio Test, and Root Test)
Write several complete simple sentences about how each series is convergent or divergent, including which test is applied !
(Hypothesis (Criteria), Conclusion (Converge/Diverge), & EXACT Test Name! )
3.
Power Series (Radius of Convergence & Interval of Convergence)
Be sure to include a check for convergence at the endpoints of the interval and write a complete simple
1 Ratio Test — Open Interval

2 Check for Convergence at the Endpoints of the Open Interval

3 Complete Simple Sentence to Conclude

4.
5.
Taylor Series & Maclaurin Series
SHOW at least first 5 nonzero terms with the correct use of 
Integration Methods
(1)Integration by Parts
(2)Trig Integral
(3)Partial Fraction
(4)Trig Substitution
(5)Completing the Square
(6)Weierstrass Substitution
6.
Definite Integral Applications
(1)Area of a Region between Two Curves
(2)Volume of Revolution Solid (Disk, Washer, & Shell)
(3)Centroid
THE END!
or 
MATH 193 (8792)
FINAL EXAM (120 PTS)
PROBLEM #1
FIND each integral or derivative (EXACT!).
1 of 6
5-20-2021(TH)
MATH 193 (8792)
FINAL EXAM (120 PTS)
5-20-2021(TH)
Show EACH Step CLEARLY!
PROBLEM #2 (
)
Write several complete simple sentences about how each series is convergent or divergent, including which test is applied !
nth-Term Test for Divergence, Geometric Series Test, p-Series Test, Integral Test, Absolute Convergence, Alternating-Series Test,
Ratio Test, Root Test, Direct Comparison Test, & Limit Comparison Test
(Hypothesis
(Criteria), Conclusion (Converge/Diverge), & EXACT Test Name!)
1.
2.
3.
2 of 6
MATH 193 (8792)
FINAL EXAM (120 PTS)
4.
5.
6.
3 of 6
5-20-2021(TH)
MATH 193 (8792)
7.
FINAL EXAM (120 PTS)
FIND the radius of convergence and the interval of convergence of the following power series.
1 Ratio Test — Open Interval

2 Check for Convergence at the Endpoints of the Open Interval

3 Complete Simple Sentence to Conclude

  1
n 1
5-20-2021(TH)
n 1
 2 x  1
n
5n n
4 of 6
MATH 193 (8792)
FINAL EXAM (120 PTS)
SHOW at least first 5 nonzero terms with the correct use of 
or 
8.
FIND the Maclaurin Series of f ( x)  cos2  3x  .
9.
FIND the Taylor Series of f ( x)  cos x  centered at a   1.
5 of 6
5-20-2021(TH)
MATH 193 (8792)
FINAL EXAM (120 PTS)
10.
FIND the following integral:
d
 sin   tan 
11.
Find the total EXACT area of the shaded region enclosed by the following given curves.
y  sin 2 x and y  cos x  6  x  32 
6 of 6
5-20-2021(TH)
MATH 193 (8792)
FINAL EXAM (120 PTS)
5-20-2021(TH)
PROBLEM #1
FIND each integral or derivative (EXACT!).
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1 of 6
15 e

MATH 193 (8792)
FINAL EXAM (120 PTS)
5-20-2021(TH)
Show EACH Step CLEARLY!
PROBLEM #2 (
)
Write several complete simple sentences about how each series is convergent or divergent, including which test is applied !
nth-Term Test for Divergence, Geometric Series Test, p-Series Test, Integral Test, Absolute Convergence, Alternating-Series Test,
Ratio Test, Root Test, Direct Comparison Test, & Limit Comparison Test
(Hypothesis
(Criteria), Conclusion (Converge/Diverge), & EXACT Test Name!)
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MATH 193 (8792)
FINAL EXAM (120 PTS)
4.

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5-20-2021(TH)

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