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

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)

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)

If you divide the circumference of a circle by the diameter, the _______ is pi.

quotient (noun)

If you divide the circumference of a circle by the diameter, the quotient is pi.

quotient (noun)

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)

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)

The straight line approaches the curve __________ but never actually touches it.

asymptote (noun)

asymptotic (adjective)

asymptotically (adverb)

The straight line approaches the curve asymptotically but never actually touches it.

asymptote (noun)

asymptotic (adjective)

asymptotically (adverb)

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)

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)

In the equation E = mc2, energy (E) is a _______ of mass (m).

function (noun)

In the equation E = mc2, energy (E) is a function of mass (m).

function (noun)

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)

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)

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)

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)

This expression may be used to introduce a problem.

Suppose we are trying to analyse the behaviour of the following function.

suppose (verb)

This expression may be used to introduce a specific example.

For instance, the limit as x goes to infinity of

for instance