Calculus Limits & Derivatives Review

Front

What is a limit in calculus?

Back

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

Front

Define continuity in a function.

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

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but the limit exists at that point.

Front

What is the formal definition of a derivative?

Back

The derivative of a function at a point is the limit of the average rate of change of the function as the interval approaches zero.

Front

Evaluate the limit: lim (x -> 2) (x^2 - 4)/(x - 2).

Back

The limit is 4.

Front

What does it mean for a limit to be infinite?

Back

A limit is infinite if the function increases or decreases without bound as it approaches a certain point.

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if f(x) ≤ g(x) ≤ h(x) for all x near a point, and the limits of f and h at that point are equal, then the limit of g at that point is also equal to that limit.

Front

Evaluate the limit: lim (x -> 0) (sin x)/x.

Back

The limit is 1.

Front

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

Back

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

Front

What is the power rule for derivatives?

Back

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