Chapter 7 - Applications of Trigonometric Functions - Section 7.1 Right Triangle Trigonometry ; Applications - 7.1 Assess Your Understanding - Page 544: 86

$0.236$ $0.243$ $0.248$

Given $f(x)=\sqrt x$, we have: For $x=5$, $\frac{f(x)-f(4)}{x-4}=\frac{f(5)-f(4)}{5-4}=\frac{\sqrt 5-\sqrt 4}{5-4}\approx0.236$ For $x=4.5$, $\frac{f(x)-f(4)}{x-4}=\frac{f(4.5)-f(4)}{4.5-4}=\frac{\sqrt {4.5}-\sqrt 4}{4.5-4}\approx0.243$ For $x=4.1$, $\frac{f(x)-f(4)}{x-4}=\frac{f(4.1)-f(4)}{4.1-4}=\frac{\sqrt {4.1}-\sqrt 4}{4.1-4}\approx0.248$