1. Determine a condition on |x − 1] that will assure that: - (a) |x² - 1|(b) |x² - 1|<1/10¯³, (c) x² - 1|<1/n for a given n = N, (d) - |x³ − 1| < 1/n for a given nЄ N.
1. Determine a condition on |x − 1] that will assure that: - (a) |x² - 1|(b) |x² - 1|<1/10¯³, (c) x² - 1|<1/n for a given n = N, (d) - |x³ − 1| < 1/n for a given nЄ N.
1. Determine a condition on |x − 1] that will assure that: - (a) |x² - 1|(b) |x² - 1|<1/10¯³, (c) x² - 1|<1/n for a given n = N, (d) - |x³ − 1| < 1/n for a given nЄ N.
Transcribed Image Text:1. Determine a condition on (x - 1| that will assure that:
(a)
|x² – 1| << //,
(b) x1 <1/10-³,
(c)
x²-1
|x² – 1| < 1/n
for a given nЄ N,
(d)x31<1/n
for a given nЄ N.
Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.
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