Limits and derivatives review

Front

What is the limit of a function as x approaches a specific value?

Back

The limit of a function as x approaches a specific value is the value that the function approaches as x gets closer to that value.

Front

Find the limit of the function as x approaches 2+.

Back

5

Front

What is the derivative of x^n?

Back

nx^(n-1)

Front

What is the derivative of a constant function, such as f(x) = 7?

Back

0

Front

What is the limit of a function that approaches a finite value?

Back

The limit is the finite value that the function approaches.

Front

What does DNE stand for in the context of limits?

Back

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

Front

What is the definition of continuity at a point?

Back

A function is continuous at a point if the limit as x approaches that point equals the function's value at that point.

Front

Find the value of c that makes the function continuous at x = 2 if f(x) = { x^2 for x < 2; c for x = 2; 3 for x > 2 }.

Back

c = 4.

Front

What is the power rule for differentiation?

Back

The power rule states that the derivative of x^n is nx^(n-1).

Front

What is the limit of a constant function?

Back

The limit of a constant function is the constant itself.