Question
Are the following statements true or false? Give reasons for tour answers.
a) -2 is a limit point of the interval 1-3,2].
b) The series is divergent.
The function, f(x)=sin² x is uniformly continuous in the interval [0, π).
d) Every continuous function is differentiable.
e) The function f defined on R by
is irrational Is integrable in the interval [2,3].
Answer :
Word Count : 567
Here are the answers along with explanations: --- ### (a) -2 is a limit point of the interval \( (1-3,2] \). False. A limit point of a set \( S \) is a point where every neighborhood contains at least one point of \( S \) different from itself. The given interval appears to be a typo—assuming you meant \( (1,3,2] \), it is not a well-defined interval. If you meant \( (1,3] \), then -2 is clearly not a limit point, since no sequence from \( (1,3] \) can approach -2. --- ### __________ ____ ____ _______ __________ ________ ______ ___ ______ __________.
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Here are the answers along with explanations: --- ### (a) -2 is a limit point of the interval \( (1-3,2] \). False. A limit point of a set \( S \) is a point where every neighborhood contains at least one point of \( S \) different from itself. The given interval appears to be a typo—assuming you meant \( (1,3,2] \), it is not a well-defined interval. If you meant \( (1,3] \), then -2 is clearly not a limit point, since no sequence from \( (1,3] \) can approach -2. --- ### __________ ____ ____ _______ __________ ________ ______ ___ ______ __________.
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