Still have math questions?

Ask our expert tutors
Trigonometry
Question

97. Here is the definition of an infinite right-h...

97. Here is the definition of an infinite right-hand limit. Suppose that an interval \(( c , d )\) lies in the domain of \(f\) . We say that \(f ( x )\) approaches infinity as \(x\) approaches \(c\) from the right, and write \(\lim _ { x \rightarrow c ^ { + } } f ( x ) = \infty\) , \(f ( x ) > B\) whenever \(c < x < c + \delta\) if, for every positive real number \(B\) , there exists a corresponding number \(\delta > 0\) such that Modify the definition to cover the following cases.

a. \(\lim _ { x \rightarrow c ^ { - } } f ( x ) = \infty\)

b. \(\lim _ { x \rightarrow c ^ { + } } f ( x ) = - \infty\)

c. \(\lim _ { x \rightarrow c ^ { - } } f ( x ) = - \infty\)

Answer

\(\left. \begin{array} { l } { \text { (a) For every positive real number } B \text { there exists a corresponding } } \\ { \text { number } \delta > 0 \text { such that for all } x } \\ { \qquad c - \delta < x < c \Rightarrow f ( x ) > B } \end{array} \right.\)

Solution
View full explanation on CameraMath App.