y = 1 + (x-1)^(1/2)
Considering the interval (2,4), calculate
delta(y) and dy.
would delta(y) be:
delta(y) = f(4) - f(2)
= (1 + squr(3) ) - 2
= squr(3) - 1
and dy is 1/(2 squr(x-1)) dx
Thank you
AGREE
thanks!
To calculate delta(y) for the given function y = 1 + (x-1)^(1/2) within the interval (2,4), you have correctly applied the formula:
delta(y) = f(4) - f(2)
= (1 + sqrt(3)) - 2
= sqrt(3) - 1
So, your calculation for delta(y) is correct.
Now, to calculate dy, which represents the differential change in y with respect to x (or the derivative of y with respect to x), you need to find the derivative of the function y = 1 + (x-1)^(1/2) using standard differentiation rules.
dy/dx = 1/(2*sqrt(x-1))
So, you are correct. The expression for dy is 1/(2*sqrt(x-1)) dx.
Let me know if there is anything else I can help you with!