One hour after a dose of a milligrams of a drug Predamestane is administered to a person, the change in body temperature T(x), in degrees Fahrenheit, is given approximately by T(x) = x² (1 − ²); for 0 ≤ x ≤ 5. The rate T'(x) at which I changes with respect to the size of the dosage is called the sensitivity of the body to the dosage.

Take h = 0.1. Use three-point centered-difference formula to approximate the first derivative of f(x)=a at x = 3. Round your answer to 3 decimal places.

Let f ( x ) = ln ⁡ ( csc ⁡ x − cot ⁡ x ). Enter the value of f ′ ( π / 2 ).

Consider a ladder sliding down a wall as in the figure. The variable a is the length of the ladder. The variable h is the height of the ladder's top at time t, and x is the distance from the wall to the ladder's bottom. Suppose that the length of the ladder is 7.7 meters and the top is sliding down the wall at a rate of 0.2 m/s. dx Calculate when h = 2.9. dt (Use decimal notation. Give your answer to three decimal places.) dx dt h=2.9 h X a m/s