Limits (Graph and Algebra)

Front

What is a limit in calculus?

Back

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

Front

Define the term 'DNE' in the context of limits.

Back

DNE stands for 'Does Not Exist', indicating that a limit does not approach a finite value.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow4}rac{x^2+3x-28}{x-4}@@.

Back

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Front

What does it mean for a limit to exist from the left?

Back

A limit exists from the left if the function approaches a specific value as the input approaches from values less than that point.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow1} f(x)@@ where f(x) is defined piecewise. What is the significance of the left-hand limit?

Back

The left-hand limit is the value that f(x) approaches as x approaches 1 from the left side.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrowrac{1}{2}}4xigg(x-rac{1}{4}igg)@@.

Back

Front

What is the limit of a polynomial function as x approaches a value?

Back

The limit of a polynomial function as x approaches a value is simply the value of the polynomial at that point.

Front

Evaluate the limit: @@ ext{lim}_{x ightarrow0}rac{x^3-6x+8}{x-2}@@.

Back

-4.

Front

What is the significance of evaluating limits at points of discontinuity?

Back

Evaluating limits at points of discontinuity helps determine the behavior of the function and whether it can be defined at that point.

Front

What is the difference between one-sided limits and two-sided limits?

Back

One-sided limits consider the approach from one direction (left or right), while two-sided limits consider both directions.