π

All Subjects

Β >Β

βΎοΈΒAP Calc

Β >Β

πUnit 1

2 min readβ’june 11, 2020

Anusha Tekumulla

The **Squeeze Theorem** (or Sandwich Theorem) is used on limit problems where the usual algebraic methods (factoring, conjugation, algebraic manipulation, or trig identities) are not effective. π₯ͺ

The actual Squeeze Theorem states that **f(x) β€ g(x) β€ h(x)** for all x in an open interval about a. **If the limit as x approaches a of f(x) = L and the limit as x approaches a of h(x) = L, then the limit as x approaches a of g(x) = L**.

With the Squeeze Theorem, we are trying to find two functions that are **1)** similar enough to the original function that we can be sure the squeeze works and **2)** easier to evaluate their limit as x β a. The theorem utilizes the statement βIf two functions squeeze together at a particular point, then any function trapped between them will get squeezed to that same point.βΒ

So, in order to use the squeeze theorem on a limit, we just have to find functions similar enough that all three functions squeeze together at a particular point like the image below.Β

**Math Warehouse**

If youβre confused, take a look at an example problem using the Squeeze Theorem.Β

As you can see in the image above, while the limit of the function in red may be hard to solve for, the similar functions in purple help us figure out that the limit of the function will still be zero. We can use this as an example.Β

First, we must confirm that f(x) β€ g(x) β€ h(x). From the graph, we can confirm that f(x) and h(x) βsqueezeβ g(x) at x = 0.Β Now we know that f(x) β€ g(x) β€ h(x), the limit as x approaches 0 of f(x)= 0, and the limit as x approaches 0 of h(x) = 0 using the graph. Thus, the limit as x approaches 0 of g(x) IS also equal to 0.

Thousands of students are studying with us for the AP Calculus AB/BC exam.

join nowBrowse Study Guides By Unit

πBig Reviews: Finals & Exam Prep

βοΈFree Response Questions (FRQ)

π§Multiple Choice Questions (MCQ)

βΎUnit 10: Infinite Sequences and Series (BC Only)

πUnit 1: Limits & Continuity

π€Unit 2: Differentiation: Definition & Fundamental Properties

π€π½Unit 3: Differentiation: Composite, Implicit & Inverse Functions

πUnit 4: Contextual Applications of the Differentiation

β¨Unit 5: Analytical Applications of Differentiation

π₯Unit 6: Integration and Accumulation of Change

πUnit 7: Differential Equations

πΆUnit 8: Applications of Integration

π¦Unit 9: Parametric Equations, Polar Coordinates & Vector Valued Functions (BC Only)

Sign up now for instant access to 2 amazing downloads to help you get a 5

Thousands of students are studying with us for the AP Calculus AB/BC exam.

join nowTake this quiz for a progress check on what youβve learned this year and get a personalized study plan to grab that 5!

START QUIZTake this quiz for a progress check on what youβve learned this year and get a personalized study plan to grab that 5!

START QUIZ