Graph the Function $\lim _ { x \rightarrow 5 } \frac { 1 } { x ^ { 2 } + 5 }$

question 224

Multiple Choice

Graph the function.Determine the limit (if it exists) by evaluating the corresponding one-sided limits. $\lim _ { x \rightarrow 5 } \frac { 1 } { x ^ { 2 } + 5 }$

• A) \(\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x ^ { 2 } + 5 } = \lim _ { x \rightarrow 5 ^ { + } } \frac { 1 } { x ^ { 2 } + 5 } = \frac { 1 } { 31 }\)
• B) \(\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x ^ { 2 } + 5 } = \lim _ { x \rightarrow 5 ^ { + } } \frac { 1 } { x ^ { 2 } + 5 } = \frac { 1 } { 14 }\)
• C) \(\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x ^ { 2 } + 5 } = \lim _ { x \rightarrow 5 ^ { + } } \frac { 1 } { x ^ { 2 } + 5 } = \frac { 1 } { 30 }\)
• D) \(\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x ^ { 2 } + 5 } = \lim _ { x \rightarrow 5 ^ { + } } \frac { 1 } { x ^ { 2 } + 5 } = - \frac { 1 } { 30 }\)
• E) \(\lim _ { x \rightarrow 5 ^ { - } } \frac { 1 } { x ^ { 2 } + 5 } = \lim _ { x \rightarrow 5 ^ { + } } \frac { 1 } { x ^ { 2 } + 5 } = - \frac { 1 } { 31 }\)

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