my homework is due in 1 hour
Let x = 1 and Δx = 0.01. Find Δy. (Round your answer to five decimal places.)
f(x) = x/x^2 + 5
To find Δy, we need to calculate the change in the value of y (Δy) when the value of x changes by Δx.
Given the function f(x) = x/x^2 + 5, we are given the values x = 1 and Δx = 0.01.
To calculate Δy, we need to find f(x+Δx) - f(x).
1. Calculate f(x):
- Substitute x = 1 into the function:
f(1) = 1 / (1^2) + 5 = 1 / 1 + 5 = 1 + 5 = 6.
2. Calculate f(x+Δx):
- Substitute x+Δx = 1 + 0.01 = 1.01 into the function:
f(1.01) = 1.01 / (1.01)^2 + 5.
3. Calculate Δy:
- Subtract f(x) from f(x+Δx):
Δy = f(1.01) - f(1).
Now, to find Δy, you'll need to evaluate f(1.01) and subtract f(1) from it by following the steps mentioned above. Finally, round the answer to five decimal places.