calculus demystified - krantz

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1、FinalExam317(c)f−1(x)=x3−x(d)f−1(x)=x/(x+1)(e)f−1(x)=x3−1a3·b−221.Theexpressionlnsimplifiestoc4/d−3(a)3lna−2lnb−4lnc+3lnd(b)3lna+2lnb+4lnc−3lnd(c)4lna−3lnb+2lnc−4lnd(d)3lna−4lnb+3lnc−2lnd(e)4lna−2lnb+2lnc+2lndlna2−lnb322.Theexpressionesimplifiesto(a)2a·3b2a(b)3b(c)a2·b3a2(d)b3(e)6a2b3
x2ifx<123.T

2、hefunctionf(x)=haslimitsxifx≥1(a)2atc=1and−1atc=0(b)1atc=1and4atc=−2(c)0atc=0and3atc=5(d)−3atc=−3and2atc=1(e)1atc=0and2atc=2x24.Thefunctionf(x)=haslimitsx2−1(a)3atc=1and2atc=−1(b)∞atc=1and0atc=−1(c)0atc=0andnonexistentatc=±1(d)2atc=−2and−2atc=2(e)−∞atc=1and+∞atc=−1
x3ifx<225.Thefunctionf(x)=√is

3、continuousatxifx≥2(a)x=2andx=3318FinalExam(b)x=2andx=−2(c)x=−2andx=4(d)x=0andx=2(e)x=2andx=2.126.Thelimitexpressionthatrepresentsthederivativeoff(x)=x2+xatc=3is[(3+h)2+(3+h)]−[32+3](a)limh→0h[(3+2h)2+(3+h)]−[32+3](b)limh→0h[(3+h)2+(3+h)]−[32+3](c)limh→0h2[(3+h)2+(3+2h)]−[32+3](d)limh→0h[(3+h)2+

4、(3+h)]−[32+4](e)limh→0hx−327.Iff(x)=thenx2+x1(a)f(x)=2x+1x2−x(b)f(x)=x−3(c)f(x)=(x−3)·(x2+x)−x2+6x+3(d)f(x)=(x2+x)2x2+6x−3(e)f(x)=x2+x28.Ifg(x)=x·sinx2then(a)f(x)=sinx2(b)f(x)=2x2sinx2(c)f(x)=x3sinx2(d)f(x)=xcosx2(e)f(x)=sinx2+2x2cosx229.Ifh(x)=ln[xcosx]thenFinalExam3191(a)h(x)=xcosx

5、xsinx(b)h(x)=xcosxcosx−xsinx(c)h(x)=xcosx(d)h(x)=x·sinx·lnxxcosx(e)h(x)=sinx30.Ifg(x)=[x3+4x]53then(a)g(x)=53·[x3+4x]52(b)g(x)=53·[x3+4x]52·(3x2+4)(c)g(x)=(3x2+4)·53x3(d)g(x)=x3·4xx3+4x(e)g(x)=2x2+131.Supposethatasteelballisdroppedfromthetopofatallbuilding.Ittakestheball7secondstohitth

6、eground.Howtallisthebuilding?(a)824feet(b)720feet(c)550feet(d)652feet(e)784feet32.Thepositioninfeetofamovingvehicleisgivenby8t2−6t+142.Whatistheaccelerationofthevehicleattimet=5seconds?(a)12ft/sec2(b)8ft/sec2(c)−10ft/sec2(d)20ft/sec2(e)16ft/sec233.Letf(x)=x3−5x2+3x−6.Thenthegraphoffis(a)concave

7、upon(−3,∞)andconcavedownon(−∞,−3)(b)concaveupon(5,∞)andconcavedownon(−∞,5)(c)concaveupon(5/3,∞)andconcavedownon(−∞,5/3)(d)concaveupon(3/5,∞)andconcavedownon(−∞,3/5)(e)concaveupon(−∞,5/3)andconcavedownon(5/3,∞)320FinalExam37234.Let