Question

3. For each of the functions below, write the differential, and calculate dy for the given values of x and dx. How accurate is dy in approximating ∆y (what is their difference) to the nearest thousandth?

Answer 1

\[f(x)= 1\div \sqrt{1+x}\] x=3 and dx=-0.04

Answer 2

I got 1/4(-0.04) but that doesnt give me 1/400 for dy

Answer 3

I got 1/4(-0.04) but that doesnt give me 1/400 for dy

Answer 4

I also need help getting delta y

Answer 5

The Total Derivative of the following expression\[y=\frac{1}{\sqrt{x+1}} \]is\[dy=-\frac{dx}{2 (x+1)^{3/2}} \]Replace dx and x with -0.04 and 3 respectively.\[dy=-\frac{-0.04}{2 (3+1)^{3/2}}= 0.0025 = \frac{25}{10000}= \frac{1}{400} \]