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Sheet2 - Math 21A Kouba Challenge Discussion Sheet 2 1...

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Unformatted text preview: Math 21A Kouba Challenge Discussion Sheet 2 1.) Write the surface area of a cube with edge length m as a function of the volume of the cube. 2.) Determine the following limits. :1: + sina: a. lim :34 sin 1 a: b. lim h ) x-—>0 ( / ) ) alt—>0— V$2 +91: _ x3—;I:2+:c——1 , _ $2+4m c.) 11m —~——-—— d.) hm arcsm w—>~oo 1—:c+:r2—:c3 :c—)oo 2x2+4 e.) lim (V 1:2 + 4:1: — V 302 — 4) f.) lim (2:1: — V :52 + 16) ZB—HDO $—)—OO 303+:c2—2zr 2 2 , ifm7é0,a:7€2 3.) Let f(:1:) = a: 1— 5’: ifsz —3, if$=2. i.) Show that f is continuous at :1: = 0. ii.) Show that f is not continuous at a: 2 2. iii.) Is f continuous for all values of :c not equal to 0 and not equal to 2 ? Why ? iv.) Sketch the graph of f. 4.) For what values of :c is each of the following functions continuous ? Briefly explain. a.) y = (3:2 + a: + 1)100 b.) f(:1:) = (In :L‘)4 + sinrr 5.) Use the Intermediate Value Theorem to prove that 5 a.) a: : m2 + 1 has at least one solution. b.) 1:4 = 33 has at least three solutions. ...
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