What are limits and derivatives in calculus?

What are limits and derivatives in calculus?

Limits are the values that a function approaches as the input approaches a certain point. Derivatives represent the rate of change of a function.

Can you explain how to calculate a limit?

To calculate a limit, you can use direct substitution, factoring, or L'Hôpital's rule if you encounter an indeterminate form.

What is the derivative of a function?

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

How do I find the derivative using the power rule?

The power rule states that if f(x) = x^n, then f'(x) = n*x^(n-1). Just multiply by the exponent and decrease the exponent by one.

What are some real-world applications of derivatives?

Derivatives are used in various fields such as physics for motion analysis, economics for cost optimization, and biology for population modeling.