Approximations

Question 1

Linear approximation

for ƒ(x) at x

Answer 1

Y – ƒ(x₁) = ƒ’(x₁) (x–x₁)

OR

L(x) = ƒ(c) + ƒ’(c) (x–c)

Question 2

Euler’s Method

for solving differential equations

Answer 2

• Solve the differential equation for dy in terms of x, y, and dx.
• Substitute values of x, y, and dx to calculate a value of dy.
• Find the approximate new value of y by adding dy to the old value of y.
• Repeat the procedure to find the next value of dy at the next value of x.

Question 3

The formula used to estimate the error in a measurement, or find the effect on a formula when a small change in measurement is made.

Answer 3

dy = ƒ’(x)•dx