Understanding L'Hopital's Rule

Understanding L'Hopital's Rule

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Hard

CCSS
HSA.APR.D.7, HSF-IF.C.7E

Standards-aligned

Created by

Mia Campbell

FREE Resource

Standards-aligned

CCSS.HSA.APR.D.7
,
CCSS.HSF-IF.C.7E
The video tutorial explains how to determine a limit using L'Hopital's Rule. It begins by identifying the indeterminate form of the limit and discusses why the initial form is not suitable for L'Hopital's Rule. The tutorial then demonstrates how to transform the function into a suitable form by finding a common denominator. After transforming the function, L'Hopital's Rule is applied twice to find the limit. The tutorial concludes with a graphical verification of the result, confirming that the limit is zero.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the initial form of the limit as x approaches 0 from the right?

Infinity minus infinity

Zero divided by zero

Infinity divided by zero

Zero minus zero

Tags

CCSS.HSA.APR.D.7

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Why can't L'Hopital's Rule be applied directly to the initial limit?

The limit is in an indeterminate form not suitable for L'Hopital's Rule

The limit is not in an indeterminate form

The limit is already determined

The limit is not in a fraction form

Tags

CCSS.HSA.APR.D.7

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the common denominator used to reformulate the problem?

x + sine x

4 + sine x

4x sine x

x sine x

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

After reformulating, what form does the limit take?

Zero divided by zero

Zero minus zero

Infinity divided by zero

Infinity minus infinity

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the derivative of 4 sine x?

4 cosine x

cosine x

4 sine x

4

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What rule is used to differentiate x sine x?

Power rule

Product rule

Quotient rule

Chain rule

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the result of applying L'Hopital's Rule for the second time?

Undefined

One

Zero

Infinity

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