Answer: 1.75
Step-by-step explanation:
To find the value of [tex]\sqrt{3}[/tex]
[tex]\text{Let , }y=\sqrt{x}[/tex]
[tex]\text{And Let x = 4 and }\Delta x=-1[/tex]
Now,
[tex]\Delta y=\sqrt{x+\Delta x}-\sqrt{x}\\\\=\sqrt{3}-\sqrt{4}=\sqrt{3}-2\\\\\Rightarrow\ \sqrt{3}=\Delta y+2[/tex]
Since dy is approximately equals to [tex]\Delta y[/tex] then ,
[tex]dy=\dfrac{dy}{dx}\Delta x\\\\=\dfrac{1}{2\sqrt{x}}\times(-1)=\dfrac{1}{2\sqrt{4}}\times(-1)=-0.25[/tex]
Thus , the approximate value of [tex]\sqrt{3}=-0.25+2=1.75[/tex]
