Disc1 - Math 21A Kouba Discussion Sheet 1 10$ - 1 1.) Use a...

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Unformatted text preview: Math 21A Kouba Discussion Sheet 1 10$ - 1 1.) Use a calculuator to determine the value of lim to three decimal places. Do 1790 .23 not use L’Hopital’s rule. 2.) Write the surface area of a sphere as a function of its volume. Use your result to find the surface area of a sphere of volume 97r cubic feet. 3.) Solve the following inequality for :r: : 23(23 ~ 1)3(a: + 2)2 S O . 4.) Determine the domain and range for each function and sketch (Do this without a graphing calculator, if possible, then check your answer with a calculator.) its graph. a.) f(x) = In: ~ 1: b.) m2) 2 la: — 1| + Irv +51 0.) f(a:) : x/cc — 3 d.) f(:c) : 172 ~ 3:1: e.) f(£l2) : 3:2 ~ 3:1: f.) 9(11) : 2sin(7r:c) g.) h(;r) : 3 + 6‘233 h.) : i.) g(:1:) : ln(:c — 4) 5.) Create (define) your own function having the following two properties : a.) Domain : all x-values ; Range : —2 S y S 2 b.) Domain : all x—values ; Range : 0 S y S 6 c.) Domain : all x-values ; Range : 1 < y < 6 (Hint: problem 4.)h.) might be of use here.) 6.) Determine all constants K so that the lim exists. Then graph the function(s). :c—l—l “58): $2+K, if$<$1 :I:+K2, ifo—l. 7.) Determine the following limits. 3~\/7~:c b. l' ) mgr—12 :1: + 2 4 . a: —1 b.) 11:3 — 1 . x + 100, 000 c.) hm ——~—— ac—)~oo ' x2 + 4 331/3 —» 1 8.) In class we “guessed” that lim : — . Verify this algebraically. meal 1 7 3317.2— 3 1 +++++++++++++++++++++++++++++++++++++++++ The following problem is for recreational purposes only‘ 9‘) Divide the following trapezoid into four (4) identical (Size and shape) pieces. 2 ...
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Disc1 - Math 21A Kouba Discussion Sheet 1 10$ - 1 1.) Use a...

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