Limits and Derivatives
Updated: November 17, 2024
Summary
The video explains how to evaluate limits using the definition of the derivative. It demonstrates finding the limit of ln x and sin x as h approaches 0 by calculating the derivative of these functions. Furthermore, it solves the limit as x approaches pi/6 of tangent x and showcases evaluating the derivative using an alternative definition. This video provides valuable insights into understanding limits and derivatives in calculus with clear and concise examples.
TABLE OF CONTENTS
Evaluation of ln x
Explaining how to evaluate the limit of ln x as h approaches 0 using the definition of the derivative.
Evaluation of sin x
Demonstrating the evaluation of the limit of sin x as h approaches 0 by finding the derivative of sine function.
Evaluation of tangent x
Solving the limit as x approaches pi/6 of tangent x and evaluating the derivative using the alternative definition of the derivative.
FAQ
Q: What method can be used to evaluate limits in calculus?
A: One method that can be used to evaluate limits in calculus is by using the definition of the derivative.
Q: How can the limit of ln x as h approaches 0 be evaluated using the definition of the derivative?
A: The limit of ln x as h approaches 0 can be evaluated using the definition of the derivative by finding the derivative of ln x with respect to x.
Q: What is the derivative of the sine function?
A: The derivative of the sine function is the cosine function.
Q: How can the limit of sin x as h approaches 0 be evaluated by finding the derivative of the sine function?
A: The limit of sin x as h approaches 0 can be evaluated by finding the derivative of the sine function and then evaluating it at the specified value of x.
Q: What is the limit as x approaches pi/6 of the tangent function?
A: The limit as x approaches pi/6 of the tangent function is tan(pi/6) which is equal to sqrt(3).
Q: How can the derivative be evaluated using the alternative definition of the derivative?
A: The derivative can be evaluated using the alternative definition of the derivative by considering a limit involving a difference quotient.
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