43. Surrounding medium of unknown temperature A pan of warm water (46°C) was put in a refrigerator. Ten minutes later, the water’s temperature was 39°C; 10 min after that, it was 33°C. Use Newton’s Law of Cooling to estimate how cold the refrigerator was.

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = e^(θ)(sinθ + cosθ)

In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.

10. y = ln(t^(3/2))

Evaluate the integrals in Exercises 33–54.

∫ (e^(√r) / √r) dr

Evaluate the integrals in Exercises 33–54.

∫(from ln3 to ln2) (e^x) dx

Solve the initial value problems in Exercises 55–58.

55. dy/dt = e^t sin(e^t − 2),y(ln 2) = 0

147. Find the area of the region between the curve y = 2x / (1 + x²) and the interval −2 ≤ x ≤ 2 of the x-axis.