Excercises 1.1


MATH is defined on any interval $I$ such that $1-\sin x>0.$ Clearly $1-\sin x\geq 0.$ Then $I$ could be any interval on which $1-\sin x\neq 0.$ e.g., MATH or MATH ...etc.

Exercises 1.2

For MATH MATH Both functions are continuous when $y^{2}-9>0.$ i.e., $y>3$ or $y<-3.$ Then the domain of continuity of both functions is MATH


Since $\left( 1,4\right) $ belongs to the domain of continuity , then Theorem 1.1 guarantees the existence of a unique solution.


Since $\left( 5,3\right) $ is not in the domain of continuity, Theorem 1.1 does not guarantee the existence or the uniqueness of a solution.

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