Dan Weinstein LaTex Work
Content
Construction of Practice Problems Activity
1. Conceptual Understanding Question: Which test BEST evaluates the convergence or divergence of the following series?
∞
•
n=2 ∞
n2 +1 5n5 +3n3 −n2 +n−7
•
n=0 ∞
2n n!
•
n=0
cos(n + 3)
2. Procedural Skills Question:
∞
How many terms of
n=0
(−1)n n+1
do you need for the remainder to be less than .00001 (ie:
1 )? 100,000
3. Multiple Representation Question: Exercise 73, Section 8.2 of Larson’s Calculus: 4. Interdisciplinary Connections Question: An Application to Marketing, Exercise 67, Section 8.2 5. Collaborative Learning Question: In groups complete the section 8.3 project on page 573. This project guides you through the
∞ 1 n n=0
proof that the harmonic series 6. Challenge Question:
diverges.
The following argument that 0 = 1 is incorrect. Explain where the error occurrs and explain this error. 0 = 0 + 0 + 0 + 0... (1) 0 = (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) . . . 0 = 1 + (−1 − 1) + (−1 + 1) + (−1 + 1) + . . . 0 = 1 + 0 + 0 + 0 + 0... 0=1 (2) (3) (4) (5)
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1. Conceptual Understanding Question: Which test BEST evaluates the convergence or divergence of the following series?
∞
•
n=2 ∞
n2 +1 5n5 +3n3 −n2 +n−7
•
n=0 ∞
2n n!
•
n=0
cos(n + 3)
2. Procedural Skills Question:
∞
How many terms of
n=0
(−1)n n+1
do you need for the remainder to be less than .00001 (ie:
1 )? 100,000
3. Multiple Representation Question: Exercise 73, Section 8.2 of Larson’s Calculus: 4. Interdisciplinary Connections Question: An Application to Marketing, Exercise 67, Section 8.2 5. Collaborative Learning Question: In groups complete the section 8.3 project on page 573. This project guides you through the
∞ 1 n n=0
proof that the harmonic series 6. Challenge Question:
diverges.
The following argument that 0 = 1 is incorrect. Explain where the error occurrs and explain this error. 0 = 0 + 0 + 0 + 0... (1) 0 = (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) . . . 0 = 1 + (−1 − 1) + (−1 + 1) + (−1 + 1) + . . . 0 = 1 + 0 + 0 + 0 + 0... 0=1 (2) (3) (4) (5)
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