Question

Find the arc length function for the curve y = 2x^(3/2) with starting point p0(9, 54).

Answer 1

To find the arc length function for the curve y = 2x^(3/2), you need to find the derivative and then use the arc length formula.

Step-by-step explanation:

To find the arc length function for the curve y = 2x^(3/2), we first need to find the derivative of the function. The derivative of y with respect to x is given by dy/dx = (3/2) * 2x^(1/2) = 3x^(1/2).

Next, we use the arc length formula, which states that the arc length of a curve y = f(x) from x = a to x = b is given by the integral of sqrt(1 + (f'(x))^2) dx.

So, the arc length function for the curve y = 2x^(3/2) is given by L(x) = ∫ sqrt(1 + (3x^(1/2))^2) dx, where L(x) is the arc length function.