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Disc4 - Math 17A Kouba Discussion Sheet 4 1 Evaluate the...

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Unformatted text preview: Math 17A Kouba Discussion Sheet 4 1.) Evaluate the following limits. ) 1, 4x3 — 7x2 + 235 — 1 ,) l' 62x + 6—235 a. 1m ——————— 1. 1m ————— x~>oo 5x3 + x2 — 5x + 1000 m—>oo e25” — e'zm _ 1:3 + 1 . . 2m —x b.) 33113100 1132 + 2 J.) m—lir—noo (6 + 6 > . 1 — CE , ex + 1 C.) $1320 x3 + a: k.) 93112100 893 + 4 , x2 —— 2x , 6—2m + 1 d') .291... 7:? 1) £131.. 67:; -m 1 e.) lim (:1: — V132 +100) m.) lim 6 + $-—>oo x..._oo 6-3: + 4 f 1, 625‘ + 1 1, e;E + 639” $13.10 623: + 4 II mirgo 62x + 63x lim 6&7 + 1 o ) lim 690 + 63$ g 33—900 621' + 4 ' mfl_oo 623: _+_ 63m 2x 1 h.) lim 6 + p.) lim (ex — V 629” + e“ ) w—>oo em + 4 - x—mo 2.) Use the Squeeze Principle (Sandwich Theorem) to evaluate the following limits. o 21: u 5 a.) lim m2s1na: b.) lim 6—33008100111 c.) lim fl $400 $ + 1 arc—>00 II-fi—OO 26$ + 1 3.) Evaluate the following limits. sin 31: sin2 4:1: tan :1: a.) 11111 b.) lim c.) lim sic—>0 55c ac—>O 3:2 92—0 a72cota: 1 — cos 3a: sin tans: sin 3:13 (1.) lim —— e.) lirn ——(——) f.) lim , m——>0 m x—mr tanm ac—>0 sma: +++++++++++++++++++++++++++++++++++++++++++ The following problem is for recreational purposes only. 4.) A snail is at the bottom of a well which is 100 feet deep. Each day it climbs up 5 feet and back down 4 feet. In how many days will the hapless snail reach the top of the well ? ...
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