Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABhardmcq1 pt

Let $f$ satisfy $\dfrac{dy}{dx} = 2y$ with $f(0) = 1$ . Using Euler's method with three steps of size $0.25$ , approximate $f(0.75)$ .

A.

3.375

B.

3

C.

4.5

D.

2.5

Explanation

Core Concept

Each step multiplies the slope by $2y$ : $1 \to 1.5 \to 2.25 \to 3.375$ after three steps of size $0.25$ .

Correct Answer

A $3.375$

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