AP Calculus AB Unit 1 Limits and Continuity Test Retake

Front

What is the definition of a limit in calculus?

Back

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

Front

What does it mean for a function to be continuous at a point?

Back

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

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow2} -x^3 + 2x^2 - 2@@

Back

-2

Front

If a function is continuous on the interval [4,7] and f(4) = 10, f(7) = 20, what can be said about f(x) for values between 10 and 20?

Back

By the Intermediate Value Theorem, there exists at least one x in [4,7] such that f(x) = 15.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow- ext{infinity}} -rac{x^4}{3x^2 - 4}@@

Back

-\infty

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow3} -rac{x^2 - 4x + 3}{x - 3}@@

Back

-2

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow ext{infinity}} -rac{x^2}{x^2 + 9}@@

Back

-1

Front

What is the Intermediate Value Theorem?

Back

The Intermediate Value Theorem states that if a function is continuous on a closed interval [a, b], then it takes every value between f(a) and f(b) at least once.

Front

What is the significance of limits approaching infinity?

Back

Limits approaching infinity indicate the behavior of a function as the input grows without bound, often revealing horizontal asymptotes.

Front

What is a removable discontinuity?

Back

A removable discontinuity occurs when a function is not defined at a point, but can be made continuous by defining it appropriately at that point.