(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

27. limit as x head towards infinity of xsin(1/x) is

A 0

B infinity

C nonexistent

D -1

E 1

from barron's ap calc 7ed, Chapter two review questions p.37

how come the answer is E? Isn't it A b/c the limit equals infinity or neg infinity times zero? the Book explains that we can represent x sin (1/x) as sin(1/x)/(1/x). when we take the limit of this, it comes out to be E.

29. a function is given, one with a removable disconinuity if x is not = 1 and y=4 when x = 1. The quesiton asks what is true? I. limf (x goes to 1) exhists? II. f(1) exhists. III. f is continuous at x = 1.

The answer turns out that I is true. how come it is not I and II?

2. Relevant equations

limits and continuity knowledge

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# Awkward limit

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