EDB — 1TN

Exercises

1. [1TN]Note:Exercise 2, written exam 4 April 2009.

   • Verify that for every \(t{\gt}1\) the equation

     \[ \sin x = x ^ t \]

     admits one and only one solution \(x{\gt}0\).

   • Call \(f(t)\) this solution, determine the image of the function \(t\) and show that it is strictly increasing and continuous on \((1,+∞)\).

   • Prove that \(f\) is extended by continuity to \(t=1\) and discuss the existence of the right derivative of the prolonged function at that point.

   Solution 1

   [1TP]↺↻