Let
x = 1
and
Δx = 0.01.
Find
Δy.
(Round your answer to five decimal places.)
f(x) = x/x^2 + 5
can someone please asap
uiuiuio
To find Δy, we need to calculate the change in the value of f(x) when x changes by Δx.
Given the function f(x) = x / (x^2 + 5), we can calculate f(x) by substituting x = 1 into the function:
f(1) = 1 / (1^2 + 5)
= 1 / (1 + 5)
= 1 / 6
= 0.1666666667 (rounded to 10 decimal places)
Now, we will calculate the value of f(x) when x changes by Δx:
f(1 + Δx) = (1 + Δx) / ((1 + Δx)^2 + 5)
= (1 + 0.01) / ((1 + 0.01)^2 + 5)
= 1.01 / (1.01^2 + 5)
≈ 1.01 / (1.0201 + 5)
≈ 1.01 / 6.0201
≈ 0.16782 (rounded to 5 decimal places)
To find Δy, subtract the initial value of f(x) from the new value:
Δy = f(1 + Δx) - f(1)
= 0.16782 - 0.1666666667
≈ 0.00116 (rounded to 5 decimal places)
Therefore, Δy ≈ 0.00116.