use differentials to approximate the value of the expression: square root of 64.07
To approximate the value of the expression √64.07 using differentials, we can start by finding the derivative of the square root function. The derivative of √x is given by:
d/dx (√x) = 1/(2√x)
Now, let's consider a small change in the value of x, which we'll call dx. We want to approximate the change in the value of √x, which we'll call dy.
dy ≈ d/dx (√x) * dx
To approximate the value of √64.07, we need to choose an appropriate value for dx. In this case, a reasonable choice would be to use a small change, such as dx = 0.07.
Now, let's substitute the values into the equation:
dy ≈ 1/(2√x) * dx
dy ≈ 1/(2√64.07) * 0.07
To simplify the expression, we can calculate the value of √64.07 and substitute it into the equation:
dy ≈ 1/(2 * 8.007) * 0.07
dy ≈ 0.00787069
Therefore, the approximate value of the expression √64.07 using differentials is approximately 0.00787069.