it: $$ lim _ { x \rightarrow 121 } \frac { 121 - x } { 11 - sqrt { x } } $$
it: $$ lim _ { x \rightarrow 121 } \frac { 121 - x } { 11 - sqrt { x } } $$
Answer
Explanation:
Step1: Rationalize the denominator
Multiply numerator and denominator by (11 + \sqrt{x}). [ \begin{align*} &\lim_{x\rightarrow121}\frac{(121 - x)(11+\sqrt{x})}{(11-\sqrt{x})(11 + \sqrt{x})}\ \end{align*} ] Since ((a - b)(a + b)=a^{2}-b^{2}), the denominator becomes (121 - x).
Step2: Simplify the expression
Cancel out the common factor (121 - x) (for (x\neq121)). [ \begin{align*} &\lim_{x\rightarrow121}\frac{(121 - x)(11+\sqrt{x})}{121 - x}\ =&\lim_{x\rightarrow121}(11+\sqrt{x}) \end{align*} ]
Step3: Substitute (x = 121)
[ \begin{align*} &11+\sqrt{121}\ =&11 + 11 \end{align*} ]
Answer:
(22)