Calculus

First Order Differential Equations

Differential Equations - Euler's Method - Step size of 1

         

Consider a function f(x)f(x) such that f(1)=4 f(1) = 4 and f(x)=x3 f'(x) = x^3 . Using Euler's method with step size 1,1, what is the resulting approximation of f(9)f(5)?f(9)-f(5)?

Consider a function f(x)f(x) satisfying f(1)=4 f(1) = 4 and f(x)=x2f'(x) = x^2 . Using Euler's method with step size 1,1, what is the resulting approximation of f(6) f(6) ?

Consider a function f(x)f(x) satisfying f(1)=3 f(1) = 3 and f(x)=1x(x+1). f'(x) = \frac{1}{x(x+1)}. Using Euler's method with step size 1,1, what is the resulting approximation of f(10) f(10) ?

Consider a function f(x)f(x) such that f(1)=5,f(x)=4x2x f(1) = 5, f'(x) = 4x^2 - x . Using Euler's method with step size 1,1, what is the value of aa that gives the approximation f(a)348f(a) \approx 348?

Consider a function f(x)f(x) such that f(1)=10 f(1) = 10 and f(x)=x2+x f'(x) = x^2 + x . Using Euler's method with step size 1,1, what is the resulting approximation of f(6)+f(12)f(6) + f(12)?

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