Calc Review 1 for the Final Exam FALL- Limits & Continuity 2024

Front

What is 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 as x approaches that point equals the function's value at that point.

Front

What is the definition of differentiability?

Back

A function is differentiable at a point if it has a defined derivative at that point, meaning it has a tangent line.

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 at that point.

Front

What is a non-removable discontinuity?

Back

A non-removable discontinuity occurs when a function cannot be made continuous at a point, often due to a jump or infinite discontinuity.

Front

What is a cusp in a function?

Back

A cusp is a point on a curve where the curve comes to a sharp point, making the function not differentiable at that point.

Front

What does it mean for a function to be continuous but not differentiable?

Back

A function can be continuous at a point but not differentiable if it has a sharp corner or cusp at that point.

Front

How do you find the limit as x approaches a value?

Back

To find the limit, evaluate the function as x gets closer to that value from both the left and right.

Front

What is the significance of limits in calculus?

Back

Limits are fundamental in defining derivatives and integrals, which are core concepts in calculus.

Front

What is the difference between continuous and differentiable functions?

Back

All differentiable functions are continuous, but not all continuous functions are differentiable.