Chapter 4: Applications of Differentiation.

4.4 Indeterminate Forms and l'Hospital's Rule.

L'hopital's Rule.

0:00 L'hopital's Rule. Indeterminate Form 0/0, inf/inf, 0 times inf, inf – inf, 0^0.

5:12 Example: lim ( X^3 + x^2 -2x )/( x – 1) as x approaches 1.

6:52 Example: lim (e^x -x – 1) /(x^2) as x approaches 0 “repeated “.

8:54 Example: lim (4 x^3 -6 x^2 +1) /(2 x^3 -10x +3) as x approaches infinity. 10:40 Example: lim ( ln x)/ (csc x) as x approaches 0+.

13:50 Example: lim (x^2) times sin (1/4 x^2) as x approaches infinity.

16:47 Example: lim ( x – sqrt (x^2 -3x)) as x approaches infinity.

21:59 Example: lim x^x as x approaches 0+.