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
Yes, you are correct.
To calculate delta(y), which represents the change in y over the interval (2,4), you can substitute x = 4 and x = 2 into the function y = 1 + (x-1)^(1/2):
delta(y) = f(4) - f(2)
= (1 + sqrt(3)) - 2
= sqrt(3) - 1
So, delta(y) is equal to sqrt(3) - 1.
To find dy, which represents the derivative of y with respect to x, you can differentiate the function y = 1 + (x-1)^(1/2) with respect to x. Applying the power rule of differentiation, we get:
dy/dx = 1/(2(sqrt(x-1)))
Therefore, dy is given by dy = 1/(2(sqrt(x-1))) dx.
So, you are correct in your calculations. Delta(y) is sqrt(3) - 1, and dy is 1/(2(sqrt(x-1))) dx.