Calculus 1-1 to 1-3 Skills Check

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 if a limit does not exist (DNE)?

Back

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

Front

Back

The limit is 7.

Front

What is the instantaneous rate of change of a function?

Back

The instantaneous rate of change is the slope of the tangent line to the curve at a given point.

Front

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

Back

Substitute the value into the function, if the function is defined at that point.

Front

What is the difference between a secant line and a tangent line?

Back

A secant line intersects the curve at two or more points, while a tangent line touches the curve at exactly one point.

Front

Back

The limit is 2.

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 as the interval approaches zero.

Front

Back

Front

What is the significance of the derivative in real-world applications?

Back

Derivatives are used to determine rates of change, such as velocity and acceleration.