Flashcards on Limits

Click on the flashcard to see the answer


What is the definition of a limit in calculus?

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

What is the difference between a limit from the left and a limit from the right?

A limit from the left is the value that a function approaches as the input approaches from the left side of a specific point, while a limit from the right is the value that a function approaches as the input approaches from the right side of the point.

What is the limit of a constant function?

The limit of a constant function is the constant itself.

What is the Squeeze Theorem used for in limits?

The Squeeze Theorem is used to find the limit of a function by comparing it to two other functions that have the same limit at a certain point, with the original function being 'squeezed' between them.

What is L'Hopital's Rule used for in limits?

L'Hopital's Rule is used to find the limit of a function that is in an indeterminate form (0/0 or infinity/infinity) by taking the derivative of the numerator and denominator and then evaluating the limit again.

What is an example of a function that does not have a limit?

An example of a function that does not have a limit would be f(x) = sin(1/x), as it oscillates infinitely between 1 and -1 as x approaches 0.

What is the definition of an infinite limit?

An infinite limit is a limit where the function approaches infinity or negative infinity as the input approaches a certain value.

What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only looks at the behavior of a function from one side of a specific point, while a two-sided limit looks at the behavior of a function from both sides of the point.

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

A limit as x approaches infinity is the value that a function approaches as x becomes infinitely large in either the positive or negative direction.

What is the limit of the function f(x) = 1/x as x approaches infinity?

The limit of the function f(x) = 1/x as x approaches infinity is 0.

What is the definition of continuity in calculus?

A function is continuous at a point if the limit of the function exists at that point and the value of the function at that point is equal to the limit.

What is the Intermediate Value Theorem used for in calculus?

The Intermediate Value Theorem is used to prove the existence of a root of a function between two points by showing that the function takes on all values between the two points.

What is the definition of a limit point in mathematics?

A limit point of a set is a point such that every neighborhood of the point contains points of the set other than the point itself.

What is the difference between a removable discontinuity and a non-removable discontinuity?

A removable discontinuity is a point at which a function is not continuous but can be made continuous by redefining the function at that point, while a non-removable discontinuity is a point at which a function is not continuous and cannot be made continuous by redefining the function at that point.

What is the definition of a one-sided limit?

A one-sided limit is a limit that only looks at the behavior of a function from one side of a specific point.

What is the definition of a limit in calculus?

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

What is the difference between a limit from the left and a limit from the right?

A limit from the left is the value that a function approaches as the input approaches from the left side of a specific point, while a limit from the right is the value that a function approaches as the input approaches from the right side of the point.

What is the limit of a constant function?

The limit of a constant function is the constant itself.

What is the Squeeze Theorem used for in limits?

The Squeeze Theorem is used to find the limit of a function by comparing it to two other functions that have the same limit at a certain point, with the original function being 'squeezed' between them.

What is L'Hopital's Rule used for in limits?

L'Hopital's Rule is used to find the limit of a function that is in an indeterminate form (0/0 or infinity/infinity) by taking the derivative of the numerator and denominator and then evaluating the limit again.

What is an example of a function that does not have a limit?

An example of a function that does not have a limit would be f(x) = sin(1/x), as it oscillates infinitely between 1 and -1 as x approaches 0.

What is the definition of an infinite limit?

An infinite limit is a limit where the function approaches infinity or negative infinity as the input approaches a certain value.

What is the difference between a one-sided limit and a two-sided limit?

A one-sided limit only looks at the behavior of a function from one side of a specific point, while a two-sided limit looks at the behavior of a function from both sides of the point.

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

A limit as x approaches infinity is the value that a function approaches as x becomes infinitely large in either the positive or negative direction.

What is the limit of the function f(x) = 1/x as x approaches infinity?

The limit of the function f(x) = 1/x as x approaches infinity is 0.

What is the definition of continuity in calculus?

A function is continuous at a point if the limit of the function exists at that point and the value of the function at that point is equal to the limit.

What is the Intermediate Value Theorem used for in calculus?

The Intermediate Value Theorem is used to prove the existence of a root of a function between two points by showing that the function takes on all values between the two points.

What is the definition of a limit point in mathematics?

A limit point of a set is a point such that every neighborhood of the point contains points of the set other than the point itself.

What is the difference between a removable discontinuity and a non-removable discontinuity?

A removable discontinuity is a point at which a function is not continuous but can be made continuous by redefining the function at that point, while a non-removable discontinuity is a point at which a function is not continuous and cannot be made continuous by redefining the function at that point.

What is the definition of a one-sided limit?

A one-sided limit is a limit that only looks at the behavior of a function from one side of a specific point.

Share


Login to Save


Share



Login to Save


Explore Other Decks


Made for Grade 10

Control and Coordination in Animals


View Deck
Made for Grade 10

Food Webs


View Deck
Made for Grade 10

Food Chain


View Deck

Explore More