Handwritten Notes

What is the limit of f(x) as x approaches a?

It indicates the value f(x) approaches as x gets close to a.

What does lim g(x) = -3 imply?

g(x) approaches -3 as x approaches a specific value.

How do you evaluate lim h(x) = 16?

Direct substitution of x into h(x) yields 16.

What happens if f(x) approaches infinity?

The function values increase without bound.

What is the result of lim (2f(x) - g(x))?

It combines the limits of f(x) and g(x) using algebraic operations.

How does direct substitution work for limits?

You replace x with the value it approaches in the function.

What does it mean if lim f(x) = DNE?

The limit does not exist due to unbounded behavior or oscillation.

What is the significance of vertical asymptotes?

They indicate points where the function approaches infinity.

How do you find the left-hand limit?

Evaluate the limit as x approaches from the left side.

What does lim f(x) = 2 signify?

As x approaches a certain value, f(x) approaches 2.

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

It describes the behavior of the function for very large x values.

What does lim g(x) = 2 indicate?

g(x) approaches 2 as x approaches a specific value.

What is the result of lim (x² + 1) as x approaches 0?

Direct substitution gives 1.

How do you evaluate limits involving square roots?

Rationalize the expression to eliminate indeterminate forms.

What does lim f(x) = ∞ mean?

The function values increase without bound as x approaches a.

What is the limit of a rational function as x approaches a point?

Evaluate by substituting the point unless it results in an indeterminate form.