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

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

Find the limits in Exercises 13–20. (If in doubt, look at the function’s graph.)

15. lim(x→∞)arctan(x)

L’Hôpital’s Rule

Find the limits in Exercises 103–110.

108. lim(x→∞)(e^x arctan(e^x))/(e^(2x)+x)

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.