evaluate the limit\nlim_{s→16} (16 - s)/(4 - √s)
evaluate the limit\nlim_{s→16} (16 - s)/(4 - √s)
Answer
Explanation:
Step1: Rationalize the denominator
Multiply numerator and denominator by $4 + \sqrt{s}$: [ \begin{align*} \lim_{s\rightarrow16}\frac{16 - s}{4-\sqrt{s}}&=\lim_{s\rightarrow16}\frac{(16 - s)(4+\sqrt{s})}{(4-\sqrt{s})(4+\sqrt{s})}\ \end{align*} ] Since $(a - b)(a + b)=a^{2}-b^{2}$, the denominator is $16 - s$. So we have $\lim_{s\rightarrow16}\frac{(16 - s)(4+\sqrt{s})}{16 - s}$.
Step2: Simplify the expression
Cancel out the common factor $16 - s$ (for $s\neq16$): [ \begin{align*} \lim_{s\rightarrow16}\frac{(16 - s)(4+\sqrt{s})}{16 - s}&=\lim_{s\rightarrow16}(4+\sqrt{s}) \end{align*} ]
Step3: Substitute the value of $s$
Substitute $s = 16$ into $4+\sqrt{s}$: [ \begin{align*} 4+\sqrt{16}&=4 + 4=8 \end{align*} ]
Answer:
$8$