Limits and Continuity

It determines the instantaneous rate of change of a function.

It allows for a direct calculation of the exact limit value.

It eliminates the need for algebraic manipulations.

It provides a visual representation of how a function behaves near a given point.

0.16393

0.16664

Undefined

0.16639

They should be random values within the domain of the function.

They should get infinitely close to the target value.

They should be integers.

They should have equal increments.

A value slightly less than the target value.

The target value itself.

Any random value within the domain of the function.

A value slightly greater than the target value.

The exact value of $g(k)$.

Positive infinity ($+\infty$)

Zero ($0$)

Negative infinity ($-\infty$)

It guarantees that the limit value will be exactly equal to the function value at the target value.

It simplifies the calculation of the limit value.

It allows us to observe the behavior of the function as x approaches the target value.

It ensures that the limit value is always zero.

The estimate becomes four times less precise due to quadratic relationship in second derivatives.

There's no significant change if all original points were equidistantly placed.

The estimate's precision doubles since larger intervals reveal broader trends.

Doubling distances makes estimates precisely twice as inaccurate due to linearity assumption failure.

To determine if a function is continuous.

To find the exact value of a limit.

To substitute the given x value into the function.

To visualize and understand the concept of limits.

6

5

3

4

Undefined

-3

-0

Zero