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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

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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)

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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)

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If you divide the circumference of a circle by the diameter, the _______ is pi. quotient (noun)

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

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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)

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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)

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The straight line approaches the curve __________ but never actually touches it. asymptote (noun) asymptotic (adjective) asymptotically (adverb)

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The straight line approaches the curve asymptotically but never actually touches it. asymptote (noun) asymptotic (adjective) asymptotically (adverb)

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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)

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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)

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In the equation E = mc 2, energy (E) is a _______ of mass (m). function (noun)

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In the equation E = mc 2, energy (E) is a function of mass (m). function (noun)

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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)

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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)

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If a term is _______, it can be ________ using the methods of _______ calculus. Thus, _________ the expression 3x 2 yields the result: 6x. differentiate (verb) differentiation (noun) differentiable (adjective) differential (adjective or noun)

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If a term is differentiable, it can be differentiated using the methods of differential calculus. Thus, differentiating the expression 3x 2 yields the result: 6x. differentiate (verb) differentiation (noun) differentiable (adjective) differential (adjective or noun)

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This expression may be used to introduce a problem. Suppose we are trying to analyse the behaviour of the following function. suppose (verb)

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This expression may be used to introduce a specific example. For instance, the limit as x goes to infinity of for instance

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TUESDAY 2.Solve the following equations. a. b. 3.Graph the line. 10x 5 -36x 14 -6r 7 = 13 + r -13 r = -6 -8 – x = -3x + x -8 = -2x x = 4.

TUESDAY 2.Solve the following equations. a. b. 3.Graph the line. 10x 5 -36x 14 -6r 7 = 13 + r -13 r = -6 -8 – x = -3x + x -8 = -2x x = 4.

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