Answer:
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General Formulas and Concepts:
<u>Calculus</u>
Limits
Limit Rule [Variable Direct Substitution]:
Special Limit Rule [L’Hopital’s Rule]:
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify given limit</em>.
<u>Step 2: Find Limit</u>
Let's start out by <em>directly</em> evaluating the limit:
- [Limit] Apply Limit Rule [Variable Direct Substitution]:
- Evaluate:
When we do evaluate the limit directly, we end up with an indeterminant form. We can now use L' Hopital's Rule to simply the limit:
- [Limit] Apply Limit Rule [L' Hopital's Rule]:
- [Limit] Differentiate [Derivative Rules and Properties]:
- [Limit] Apply Limit Rule [Variable Direct Substitution]:
- Evaluate:
∴ we have <em>evaluated</em> the given limit.
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Learn more about limits: brainly.com/question/27807253
Learn more about Calculus: brainly.com/question/27805589
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Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits