47. Carbon-14 The oldest known frozen human mummy, discovered in the Schnalstal glacier of the Italian Alps in 1991 and called Otzi, was found wearing straw shoes and a leather coat with goat fur, and holding a copper ax and stone dagger. It was estimated that Otzi died 5000 years before he was discovered in the melting glacier. How much of the original carbon-14 remained in Otzi at the time of his discovery?

Indeterminate Powers and Products

Find the limits in Exercises 53–68.

53. lim (x → 1⁺) x^(1/(1 - x))

"In Exercises 59–86, find the derivative of y with respect to the given independent variable.

67. y = 7^(sec θ) ln 7"

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

45. y=cos(x-arccos(x))

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

23. y = ln(x)/(1+ln(x))

Use the results of Exercise 55 to show that the functions in Exercises 56–60 have inverses over their domains. Find a formula for df⁻¹/dx using Theorem 1.

f(x) = 27x³

Solve the differential equation in Exercises 9–22.

9. 2√(xy) (dy/dx) = 1, x, y > 0