Evaluating Limits and Expressions

Evaluating Limits and Expressions

Assessment

Interactive Video

Mathematics

9th - 10th Grade

Hard

Created by

Thomas White

FREE Resource

The video tutorial explains how to find limits in calculus when direct substitution results in an indeterminate form like 0/0. It demonstrates two examples: one involving factoring a quadratic expression and another using the difference of cubes. The first example shows how to factor the numerator to cancel terms and find the limit. The second example involves factoring the difference of cubes to simplify the expression and determine the limit. The video emphasizes the importance of recognizing when substitution leads to indeterminate forms and using algebraic techniques to resolve them.

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15 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result when you directly substitute -3 into the expression -3^2 + -3 - 6 over -3 + 3?

0/0

1/1

1/0

0/1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the indeterminate form 0/0 suggest about the limit?

The limit is infinite

Further simplification is needed

The limit is zero

The limit does not exist

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How can the expression x^2 + x - 6 be factored?

(x + 3)(x - 2)

(x - 3)(x + 2)

(x + 2)(x - 1)

(x - 2)(x - 3)

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After canceling the common terms, what expression is left to evaluate the limit as x approaches -3?

x + 3

x - 3

x - 2

x + 2

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the final limit of the expression as x approaches -3?

0

-3

-5

5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What happens to the terms x + 3 in the first example after factoring?

They are multiplied

They are added

They are canceled

They are subtracted

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the significance of the expression x - 2 in the first example?

It is the final limit

It is the original expression

It is the factor that cancels

It is the indeterminate form

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