Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule

1. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Indeterminate Forms L’Hopital’s Rule If then If then

2. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Indeterminate Forms

3. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Indeterminate Forms

4. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Other Indeterminate Forms

5. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Other Indeterminate Forms Find a common denominator

6. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Other Indeterminate Forms – Indeterminate Powers = )

7. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Other Indeterminate Forms – Indeterminate Powers:

8. Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Other Indeterminate Forms – Indeterminate Powers:

9. Sec 4.6 – Applied Optimization 1) The position function of a projectile launched vertically upward from an elevated position is . Position (s) is measured in feet and time (t) is measured in seconds. a) When will the projectile hit the ground? b) What is the impact velocity? c) When will the projectile reach its maximum height? d) What is its maximum height? 2) A cardboard box manufacturing company has to maximize the volume of a box made from a 24-inch by 9-inch sheet of cardboard. What are the dimensions of the box? 3) A box is to be constructed where the base length is 3 times the base width.  The material used to build the top and bottom cost $10 per square foot and the material used to build the sides cost $6 per square foot.  If the box must have a volume of 50 cubic feet, determine the dimensions that will minimize the cost to build the box. 4) A printer need to make a poster that will have a total area of 200 in2 and will have 1 inch margins on the sides, a 2 inch margin on the top and a 1.5 inch margin on the bottom.  What dimensions will give the largest printed area?