First Order Differential Equations
Consider a function \(f(x)\) such that \( f(1) = 4\) and \( f'(x) = x^3 \). Using Euler's method with step size \(1,\) what is the resulting approximation of \(f(9)-f(5)?\)
Consider a function \(f(x)\) satisfying \( f(1) = 4\) and \(f'(x) = x^2 \). Using Euler's method with step size \(1,\) what is the resulting approximation of \( f(6) \)?
Consider a function \(f(x)\) satisfying \( f(1) = 3\) and \( f'(x) = \frac{1}{x(x+1)}. \) Using Euler's method with step size \(1,\) what is the resulting approximation of \( f(10) \)?
Consider a function \(f(x)\) such that \( f(1) = 5, f'(x) = 4x^2 - x \). Using Euler's method with step size \(1,\) what is the value of \(a\) that gives the approximation \(f(a) \approx 348\)?
Consider a function \(f(x)\) such that \( f(1) = 10\) and \( f'(x) = x^2 + x \). Using Euler's method with step size \(1,\) what is the resulting approximation of \(f(6) + f(12)\)?