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Pre-Calc Homework Solutions 265

Pre-Calc Homework Solutions 265 - Quick Review 6.5 1 All...

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The right side of the differential equation is: mg 2 kv 2 5 mg 2 k 1 } m k g } 21 1 2 } e 2 at 2 1 1 } 2 2 5 mg 3 1 2 1 1 2 } e 2 at 2 1 1 } 2 2 4 5 mg 1 1 2 1 1 } e 2 at 4 1 1 } 2 } ( e 2 at 4 1 1) 2 } 2 5 mg } 4( e ( e 2 a 2 t a 1 t 1 1 1 ) ) 2 2 4 } 5 } ( 4 e 2 m at g 1 e 1 2 a ) 2 t } Since the left and right sides are equal, the differential equation is satisfied. And v (0) 5 ! } m k § g } § } e e 0 0 2 1 e e 0 0 } 5 0, so the initial condition is also satisfied. (b) lim t v ( t ) 5 lim t 1 ! } m k § g } § } e e a a t t 2 1 e e 2 2 a a t t } ? } e e 2 2 a a t t } 2 5 lim t 1 ! } m k § g } § } 1 1 2 1 e e 2 2 2 2 a a t t } 2 5 ! } m k § g } § 1 } 1 1 2 1 0 0 } 2 5 ! } m k § g } § The limiting velocity is ! } m k § g } § . (c) ! } m k § g } § 5 ! } 0 1 § .0 6 § 0 0 § 5 } § < 179 ft/sec The limiting velocity is about 179 ft/sec, or about 122 mi/hr. Section 6.5 Population Growth (pp. 342–349)
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Unformatted text preview: Quick Review 6.5 1. All real numbers 2. lim x → ‘ f ( x ) 5 } 1 5 1 } 5 50 lim x → 2‘ f ( x ) 5 3. y 5 0, y 5 50 4. In both f 9 and f , the denominator will be a power of 1 1 5 e 2 0.1 x , which is never 0. Thus, the domains of both are all real numbers. 5. [ 2 30, 70] by [ 2 10, 60] f ( x ) has no zeros. Section 6.5 265...
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