indeterminate forms and l’hospital’s rule vocabulary preview based on:: stewert, j. (2008)....
TRANSCRIPT
![Page 1: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/1.jpg)
Indeterminate Forms and L’Hospital’s Rule
Vocabulary Preview
Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307. Belmont, CA: Thomson
![Page 2: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/2.jpg)
As the variable x approaches the ___________ a, both the numerator and denominator approach zero. This means that the expression is indeterminate at a.
limit (noun or verb)
limited (adjective)
limiting (adjective)
![Page 3: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/3.jpg)
As the variable x approaches the limit a, both the numerator and denominator approach zero. This means that the expression is indeterminate at a.
limit (noun or verb)
limited (adjective)
limiting (adjective)
![Page 4: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/4.jpg)
If you divide the circumference of a circle by the diameter, the _______ is pi.
quotient (noun)
![Page 5: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/5.jpg)
If you divide the circumference of a circle by the diameter, the quotient is pi.
quotient (noun)
![Page 6: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/6.jpg)
In Mathematics, a ________ number is a number that can be expressed as a ratio of whole numbers. Series and functions can also be ________.
rational (adjective or noun)
![Page 7: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/7.jpg)
In Mathematics, a rational number is a number is a number that can be expressed as a ratio of whole numbers. Series and functions can also be rationals.
rational (adjective or noun)
![Page 8: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/8.jpg)
The straight line approaches the curve __________ but never actually touches it.
asymptote (noun)
asymptotic (adjective)
asymptotically (adverb)
![Page 9: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/9.jpg)
The straight line approaches the curve asymptotically but never actually touches it.
asymptote (noun)
asymptotic (adjective)
asymptotically (adverb)
![Page 10: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/10.jpg)
The workers wanted an increase of two dollars an hour. The management offered one dollar an hour extra. After much deliberation, the two sides reached a _________ and agreed on an increase of $1.50 an hour.
compromise (verb or noun)
compromising (adjective)
compromised (adjective)
![Page 11: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/11.jpg)
The workers wanted an increase of two dollars an hour. The management offered one dollar an hour extra. After much deliberation, the two sides reached a compromise and agreed on an increase of $1.50 an hour.
compromise (verb or noun)
compromising (adjective)
compromised (adjective)
![Page 12: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/12.jpg)
In the equation E = mc2, energy (E) is a _______ of mass (m).
function (noun)
![Page 13: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/13.jpg)
In the equation E = mc2, energy (E) is a function of mass (m).
function (noun)
![Page 14: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/14.jpg)
If you raise a number to a certain _______, such as x, you multiply it times itself x times. Thus, 4 to the ______ of 3 is 4 X 4 X 4 = 64.
(to the) power (of) (noun)
![Page 15: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/15.jpg)
If you raise a number to a certain power, such as x, you multiply it times itself x times. Thus, 4 to the power of 3 is 4 X 4 X 4 = 64.
(to the) power (of) (noun)
![Page 16: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/16.jpg)
If a term is _______, it can be ________ using the methods of _______ calculus. Thus, _________ the expression 3x2 yields the result: 6x.
differentiate (verb)
differentiation (noun)
differentiable (adjective)
differential (adjective or noun)
![Page 17: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/17.jpg)
If a term is differentiable, it can be differentiated using the methods of differential calculus. Thus, differentiating the expression 3x2 yields the result: 6x.
differentiate (verb)
differentiation (noun)
differentiable (adjective)
differential (adjective or noun)
![Page 18: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/18.jpg)
This expression may be used to introduce a problem.
Suppose we are trying to analyse the behaviour of the following function.
suppose (verb)
![Page 19: Indeterminate Forms and L’Hospital’s Rule Vocabulary Preview Based on:: Stewert, J. (2008). Calculus: Early Transcendentals (6th ed.), pp. 298-299, 307](https://reader035.vdocuments.net/reader035/viewer/2022062219/551b3bce550346d41a8b545d/html5/thumbnails/19.jpg)
This expression may be used to introduce a specific example.
For instance, the limit as x goes to infinity of
for instance