Evaluate the Limit

Problem

(lim_x→−7)((7−|x|)/(7+x))

Solution

1. Analyze the absolute value expression |x| as x approaches −7 Since x is approaching a negative value, we use the definition |x|=−x for x<0

2. Substitute the definition of the absolute value into the limit expression.

(lim_x→−7)((7−(−x))/(7+x))

3. Simplify the numerator by distributing the negative sign.

(lim_x→−7)((7+x)/(7+x))

4. Reduce the fraction by dividing the numerator and denominator by the common factor (7+x) noting that x≠−7 as we approach the limit.

(lim_x→−7)(1)

5. Evaluate the limit of the constant.

1

Final Answer

(lim_x→−7)((7−|x|)/(7+x))=1

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