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Calculus / Thomas' Calculus: Early Transcendentals 13 / Chapter 2 / Problem 6AAE

Thomas' Calculus: Early Transcendentals | 13th Edition | ISBN: 9780321884077 | Authors: George B. Thomas Jr., Maurice D. Weir, Joel R. Hass

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Chapter 2, Problem 6AAE

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QUESTION:

PROBLEM 6AAE

Stripes on a measuring cup The interior of a typical 1-L measuring cup is a right circular cylinder of radius 6 cm (see accompanying figure). The volume of water we put in the cup is therefore a function of the level h to which the cup is filled, the formula being How closely must we measure h to measure out 1 L of water (1000 cm3) with an error of no more than 1% (10 cm3) ?

A 1-L measuring cup (a), modeled as a right circular cylinder (b) of radius r = 6cm

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QUESTION:

PROBLEM 6AAE

Stripes on a measuring cup The interior of a typical 1-L measuring cup is a right circular cylinder of radius 6 cm (see accompanying figure). The volume of water we put in the cup is therefore a function of the level h to which the cup is filled, the formula being How closely must we measure h to measure out 1 L of water (1000 cm3) with an error of no more than 1% (10 cm3) ?

A 1-L measuring cup (a), modeled as a right circular cylinder (b) of radius r = 6cm

ANSWER:

Solution:

Step 1 of 2:

In this problem, we need to find the value of the given limit $\lim\limits_{{x\ } \rightarrow {0}}g(x).$

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