calculate delta y for f(x)= x^(3/2) with x= 4 and delta x= dx=0.1
delta y= f(x+delta x)- f(x)
= f(4.1) - f(4)
delta y= f(4.1)-8
f(x + delta x)= 8 + 3/2*x^(1/2)*0.1
= 8 + 0.15x^(1/2)
= 8 + 0.30
= 8.30
delta y= 8.30 - 8
delta y= 0.30
but this is wrong. why is it wrong?
Hmm. Looks good to me. But you've done a lot of extra work. Using differentials, we approximate delta y = dy
dy = f'(x) dx
= 3/2 x^(1/2) dx
= 3/2 (2) (.1)
= 0.3
The calculations provided are incorrect. Here is the correct way to calculate delta y for the function f(x) = x^(3/2) with x = 4 and delta x = 0.1:
First, let's substitute the given values into the equation for delta y:
delta y = f(x + delta x) - f(x)
f(x + delta x) = (x + delta x)^(3/2) = (4 + 0.1)^(3/2) = 4.1^(3/2)
f(x) = x^(3/2) = 4^(3/2) = 8
Now, let's calculate the values:
delta y = 4.1^(3/2) - 8
To perform this calculation, we need to express 4.1 as an exact square root and then raise it to the power of (3/2):
4.1 = 4 + 0.1 = 2^2 + 0.1 = (2 + 0.1)^2 = 2.1^2
Using this value, we can now calculate delta y:
delta y = (2.1^2)^(3/2) - 8
Simplifying further:
delta y = 2.1^3 - 8
Using a calculator, we find:
delta y ≈ 9.261 - 8 ≈ 1.261