it: \\( \\lim _ { x \\rightarrow 1 } \\frac { 3 - 3 x } { 1 - \\sqrt { x } } \\)
it: \\( \\lim _ { x \\rightarrow 1 } \\frac { 3 - 3 x } { 1 - \\sqrt { x } } \\)
Answer
Explanation:
Step1: Factor numerator and rationalize denominator
Factor numerator: (3 - 3x=3(1 - x)=3(1-\sqrt{x})(1 + \sqrt{x})). The original limit becomes (\lim_{x\rightarrow1}\frac{3(1 - \sqrt{x})(1+\sqrt{x})}{1-\sqrt{x}}).
Step2: Simplify the expression
Cancel out the common factor ((1 - \sqrt{x})) (for (x\neq1)), we get (\lim_{x\rightarrow1}3(1+\sqrt{x})).
Step3: Substitute (x = 1)
Substitute (x = 1) into (3(1+\sqrt{x})), we have (3(1+\sqrt{1})).
Answer:
(6)