Question

Let y=2 √{x} . Find the change in y, δy when x=4 and δ x=0.2 . Find the differential d y when x=4 and d x=0.2

Answer 1

When x = 4 and δx = 0.2, the change in y (δy) is approximately 0.098. The differential dy when x = 4 and dx = 0.2 is also approximately 0.098.

Step-by-step explanation:

To find the change in y (δy) when x = 4 and δx = 0.2, we can use the equation y = 2√(x).

First, substitute the given values into the equation:

y = 2√(4) = 2(2) = 4.

Next, find the change in y by substituting the new value of x and δx into the equation:

δy = 2√(4 + 0.2) - 2√(4) = 2√(4.2) - 4 = 2(2.049) - 4 ≈ 0.098.

Now, to find the differential dy when x = 4 and dx = 0.2:

dy ≈ δy = 0.098.