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Calculus

First Order Differential Equations

Concept Quizzes

Differential Equations - Formulate a Statement
Differential Equations - Degree and Order
Differential Equations - Euler's Method - Step size of 1
Differential Equations - dy/dx = f(x)
Differential Equations - dy/dx = g(y)
Differential Equations - Variable Separable
Logistic Differential Equations
Differential Equations - Modeling

Challenge Quizzes

First Order Differential Equations: Level 2 Challenges

Differential Equations - 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 $f(9)-f(5)?$

1196 1770 1470 948

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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 $f(6)$ ?

59 47 49 81

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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 $f(10)$ ?

\frac{39}{10}

\frac{10}{3}

\frac{37}{10}

\frac{39}{11}

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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 $f(a) \approx 348$ ?

7 6 9 8

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

652 662 667 657

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