evaluate the limit\nlim(x→49) (49 - x)/(7 - √x)
evaluate the limit\nlim(x→49) (49 - x)/(7 - √x)
Answer
Explanation:
Step1: Rationalize the denominator
Multiply numerator and denominator by $7 + \sqrt{x}$. [ \begin{align*} \lim_{x\rightarrow49}\frac{49 - x}{7-\sqrt{x}}\times\frac{7+\sqrt{x}}{7+\sqrt{x}}&=\lim_{x\rightarrow49}\frac{(49 - x)(7+\sqrt{x})}{49 - x} \end{align*} ]
Step2: Simplify the expression
Cancel out the common factor $49 - x$. [ \begin{align*} \lim_{x\rightarrow49}\frac{(49 - x)(7+\sqrt{x})}{49 - x}&=\lim_{x\rightarrow49}(7+\sqrt{x}) \end{align*} ]
Step3: Evaluate the limit
Substitute $x = 49$ into $7+\sqrt{x}$. [ 7+\sqrt{49}=7 + 7=14 ]
Answer:
$14$