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The water should fill the aquarium to 1.5 feet
Solution:
Given that the directions for the aquarium say that it should be filled with 9 cubic feet of water.
This means volume of aquarium is 9 cubic feet
Given that aquarium is 2 feet wide and 3 feet long
To find: Height of aquarium
Since a aquarium is in shape of cuboid, we can use the volume of cuboid formula
<em><u>The volume of cuboid is given as:</u></em>
volume of cuboid =
Where "l" is the length
w is the width
"h" is the height
Substituting the values, we get,
Thus the height of aquarium is 1.5 feet
Answer:
4) The limit does not exist.
General Formulas and Concepts:
<u>Calculus</u>
Limits
- Right-Side Limit:
- Left-Side Limit:
Limit Rule [Variable Direct Substitution]:
Step-by-step explanation:
*Note:
For a limit to exist, the right-side and left-side limits must be equal to each other.
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Find Left-Side Limit</u>
- Substitute in function [Left-Side Limit]:
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
<u>Step 2: Find Left-Side Limit</u>
- Substitute in function [Right-Side Limit]:
- Evaluate limit [Limit Rule - Variable Direct Substitution]:
∴ since ,
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits