Chapter 8.4, Problem 18ES

Consider the slope field in Exercise 15.

(a) Use Euler’s Method with $\Delta x=0.1$ to estimate $y\left(\frac{1}{2}\right)$ for the solution that satisfies the initial condition $y(0)=1.$

(b) Would you conjecture your answer in part (a) to be greater than or less than the actual of $y\left(\frac{1}{2}\right)?$ Explain.

(c) Check your conjecture in part (b) by finding the exact value of $y\left(\frac{1}{2}\right).$