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A study guide for the final exam of Math 312: Real Analysis at Penn State University. The exam covers material from Chapters 1 through 17 from the textbook. The study guide includes definitions related to sequences and/or functions, and questions with proper justification. useful for students preparing for the final exam in Real Analysis.
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Penn State University Section 001
The final exam is scheduled for Monday, December 15, from 8:00am to 9:50am in 102 Chem. The exam will cover material from Chapters 1 through 17 from our textbook. Material from Chapter 22 will be covered during the last week of classes, but will not appear on the final exam. All questions on the final exam will come from this study guide. While solutions will not be posted, I will be more than happy to discuss possible solutions to these problems during office hours. Students will be expected to know the following definitions as they relate to sequences and/or functions.
√n) (c) lim n→∞
√sin(1/n)
n=
an converges to L. Show that
n=
(a 2 n + a 2 n+1) also converges to L.
(a)
n=
n^3 xn^ (b)
n=
3 n n^3 x
3 n (^) (c) ∑^ ∞ n=
(3 + (−1)n)nxn
x^2 if x is rational 0 if x is irrational is differentiable at 0 and not differentiable everywhere else.