At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Ask your questions and receive accurate answers from professionals with extensive experience in various fields on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
We are given the following differential equation:
[tex]\frac{dy}{dx}=\frac{x(y-1)}{4}[/tex]Since this equation gives the value of the slope of the tangent line at any point (x,y). To determine the equation of such line we need to use the general form of a line equation:
[tex]y=mx+b[/tex]Since in a tangent line the slope is equivalent to the derivative we may replace that into eh line equation like this:
[tex]y=\frac{dy}{dx}x+b[/tex]Now we determine the value of dy/dx at the point (1,3):
[tex]\frac{dy}{dx}=\frac{(1)(3-1)}{4}=\frac{2}{4}=\frac{1}{2}[/tex]Replacing into the equation of the line:
[tex]y=\frac{1}{2}x+b[/tex]Now we replace the point (1,3) to get the value of "b":
[tex]3=\frac{1}{2}(1)+b[/tex]Solving for "b":
[tex]\begin{gathered} 3=\frac{1}{2}+b \\ 3-\frac{1}{2}=b \\ \frac{5}{2}=b \end{gathered}[/tex]Replacing into the line equation:
[tex]y=\frac{1}{2}x+\frac{5}{2}[/tex]And thus we get the equation of the tangent line.
To approximate the value of f(1.4) we replace the value x = 1.4 in the equation of the tangent line:
[tex]y=\frac{1}{2}(1.4)+\frac{5}{2}[/tex]Solving the operation:
[tex]y=3.2[/tex]Therefore, the approximate value of f(1.4) is 3.2
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
