(c.) \\( \\lim _ { x \\rightarrow 3 ^ { - } } \\frac { 7 x - 21 } { | x - 3 | } \\)
(c.) \\( \\lim _ { x \\rightarrow 3 ^ { - } } \\frac { 7 x - 21 } { | x - 3 | } \\)
Answer
Explanation:
Step1: Analyze the absolute - value function for (x\to3^{-})
When (x\to3^{-}), then (x - 3\lt0). So, (|x - 3|=-(x - 3)). The limit becomes (\lim_{x\to3^{-}}\frac{7x - 21}{-(x - 3)}).
Step2: Factor the numerator
Factor (7x-21) as (7(x - 3)). Then the limit is (\lim_{x\to3^{-}}\frac{7(x - 3)}{-(x - 3)}).
Step3: Simplify the expression
Cancel out the non - zero factor ((x - 3)) (since (x\neq3) when taking the limit). We get (\lim_{x\to3^{-}}\frac{7}{-1}).
Answer:
(-7)