Question

Consider the differential equation. Use linear approximation (Euler's method) with two steps to estimate when:

A) The exact solution
B) The average rate of change
C) The limit of the function
D) The tangent line to the curve at a specific point

Answer 1

Euler's method, also known as linear approximation, is used to estimate the solution of a differential equation. It involves dividing the interval into smaller steps and approximating the solution at each step.

Step-by-step explanation:

Euler's method, also known as linear approximation, is used to estimate the solution of a differential equation. It involves dividing the interval into smaller steps and approximating the solution at each step.

To estimate when the exact solution, average rate of change, limit of the function, and tangent line to the curve at a specific point, you would use Euler's method with two steps:

1. Choose an initial value for the solution.
2. Use the given differential equation to find the slope at the initial point.
3. Use the slope to estimate the solution at the next step using the formula: yi+1 = yi + h*f(xi, yi), where yi+1 is the estimated solution at the next step, yi is the solution at the current step, h is the step size, f(xi, yi) is the value of the differential equation at the current step, and xi is the x-coordinate at the current step.
4. Repeat step 3 for the second step to estimate the solution at the desired time.