Calculus Limits Practice Test

Front

What is a limit in calculus?

Back

A limit is a value that a function approaches as the input approaches some value. It is fundamental in defining derivatives and integrals.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow1} (3x + 1)@@

Back

4

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow-1^-} (x^2 - 1)@@

Back

0

Front

What does it mean if a limit does not exist?

Back

A limit does not exist if the function approaches different values from the left and right sides, or if it approaches infinity.

Front

Evaluate f(6) if f(x) = 2x - 5.

Back

f(6) = 7

Front

What is the product of the polynomials (7y + 4)(8y + 2)?

Back

56y^2 + 46y + 8

Front

Define continuity at a point in calculus.

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

Back

One-sided limits consider the behavior of a function as it approaches a point from one side (left or right), while two-sided limits consider both sides.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow2} (x^2 - 4)/(x - 2)@@

Back

4

Front

What is the Squeeze Theorem?

Back

The Squeeze Theorem states that if a function is squeezed between two other functions that have the same limit at a point, then the squeezed function also has that limit.