AP Calculus Review #1 (Limits and Derivatives)

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value.

Front

What does DNE stand for in the context of limits?

Back

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.

Front

How do you find the limit of a function as x approaches a specific value?

Back

To find the limit, substitute the value into the function if it is continuous at that point, or use limit laws.

Front

What is the limit of a function as x approaches -4 from the left if the limit is 2?

Back

The limit is 2, meaning the function approaches 2 as x gets closer to -4 from the left.

Front

What is the second derivative of the function f(x) = 2x - 5x^6?

Back

f''(x) = -150x^4.

Front

What is the derivative of -cot(x)?

Back

The derivative of -cot(x) is csc^2(x).

Front

What is the definition of a derivative?

Back

A derivative represents the rate of change of a function with respect to a variable.

Front

What is the power rule for differentiation?

Back

The power rule states that d/dx[x^n] = n*x^(n-1), where n is a constant.

Front

What is the limit of a constant function?

Back

The limit of a constant function as x approaches any value is the constant itself.

Front

What is the difference between one-sided limits and two-sided limits?

Back

One-sided limits approach a value from one direction (left or right), while two-sided limits approach from both directions.