2A_midterm1_samp

2A_midterm1_samp - if it exists. If it does not exist,...

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a Math 2A : SamPle Midterm # I This exam consists of 4 questions worth I0 points eqch and 4 questions worth I5 points each. Read directions for each problem carefully. Please show all work needed to arrive at your solutions. Label graphs. Clearly indicate yourfinal answers. 1,) Mark each of the following statements as true or false. (No work needs to be shown.) a.) lf f is a continuous function and /(1) ) 0 and /(5) < 0, then there exists a number c between I and 5 such that f (c) = O' True False b.) Ifl iscontinuousat5 and f(5) =2andf @) = 3,thenlimv-z f @xz -rr) =2' True False . d,t ,) hlxz + xl = lZx * Ll True False d.) If limr-s f (x) = 0 and limr-s g@) = 0, then lim'-s I ao. . not exist. ^ " qlx) True False e,) lf f is differentiable at a, then / is continuous at a' True Fqlse 2.) A graph of a function g(f) is given below' Sketch a possible graph of g'(t)'
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3.) For the function h whose graph is given, state the value of each quantity,
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Unformatted text preview: if it exists. If it does not exist, explain why. a.) limr-6- h(x) = b.) lim's+ h(x) = c.) limlro h(x) = d.) h(0) = e.) lim'-2- h(x) = f.) limr-2+ h(x) = g.) limr-2 h(x) = h.) h(2)= i.) lim,--2 h(x): j.) limr-3 h(x) = 4.) If gas in a cylinder is maintained at a constant temperature 7, the pressure P is related to the volu J V by a formula of the form nRT anz P --' V-nb Vz in which a,b,nand R are constants. findffiand explain what this quantity would mean physically, ,( 1**-t-1 &quot;3 ''t &quot;13 5.) Evaluate the limit, if it exists. x2+x-6 a.) ltmx-Z ,1 b.) limr-7 ^ltfr-z t-7 c.) limr--2 r. +3r 6.) Using the definition of derivative, find f' (x) for the function f (x) = x2 - 4x - B. 7.) Calculate y' for each of the following. a')Y=xa-sx2+x b.) y=i c) Y=rli d.) Y=tz e') Y = cosx 8.) Calculate y' for each of the following. a.)y=(x3-3x)sed(k) b.) y = sin(g) tan(g) V03 ,2t c.)y=fr...
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This note was uploaded on 12/07/2010 for the course MATH MATH 2A taught by Professor Alessandrapantano during the Fall '10 term at UC Irvine.

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2A_midterm1_samp - if it exists. If it does not exist,...

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