×

## First Order Differential Equations

These are equations, Calculus-style. From modeling real-world phenomenon, from the path of a rocket to the cooling of a physical object, Differential Equations are all around us.

# Euler's Method - Step Size of 1

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 $$f(6) + f(12)$$?

×