Limits & Derivatives

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Find the derivative of the function f(x) = -4x.

Back

f'(x) = -4.

Front

What is the definition of a limit in calculus?

Back

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

Front

Find the derivative of the function f(x) = 5x^4.

Back

f'(x) = 20x^3.

Front

Evaluate the limit: \( \lim_{x\rightarrow3}\sqrt{x^2-4} \)

Back

The limit is \( \sqrt{5} \).

Front

What is the power rule for differentiation?

Back

If f(x) = x^n, then f'(x) = nx^(n-1).

Front

What is the limit of a function as x approaches infinity?

Back

The limit can be finite, infinite, or may not exist (DNE) depending on the function.

Front

Find the derivative of f(x) = 7x^2 + 3x - 5.

Back

f'(x) = 14x + 3.

Front

What is the derivative of f(x) = e^x?

Back

f'(x) = e^x.

Front

What does DNE stand for in limits?

Back

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