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HW 1.11 Practice Test solutions

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School
Western University**We aren't endorsed by this school
Course
CALCULUS 1000
Subject
Mathematics
Date
Dec 18, 2024
Pages
12
Uploaded by harika204
PRACTICE1.Find the numbers for x where the function below is not continuous. Explain what type of discontinuity (if any) ispresent.2.Find the slope of the tangent to the graph of!(#) = √# − 3at P(4,1).64224685523infinitediscontinuityKIjumpdiscontinuityx3pointremovablediscontinuityHANyEM1infC4thlhhsoTEIlimhhsohFhimto2nsohis1limnsoHass1sisI2ofTheslopeofthetangentismI2
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3.Evaluate the following limits, if possible.a))*+# → 1./012/134/01.b))*+# → 24/01/136/017c))*+# → 3/81239/01./14d))*+# → 3√# − 3e))*+# → −2:;<:8/=<>7f))*+# → 27/19@/:=145472847132himxt5Xk2CD5z.gsxt2I3ulimz4so26522214aCx4alin533xS321XxIozGetsCxiaD3 3349Gtaa6187tfKLabLetxaeasetea413Chim64a327321inATa7372444447416Ca43a19lin2a53CHlimyes243424269919L2784811618128L2241224494toIEpasay
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5. Analyze the continuity of this function and state any discontinuities.221( )41333xxxf xxxxxì+£ï=-<<íï-³î1inx421212xS531in4x42fCxiscontinuousatx asaget3fGH231in4x43xS3atinhasatisnotcontinuousatx351of3O
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6. Consider the following position function of a particle in motion:A(B) = 2B9− 9B + 4,wheres(t)represents the position in metres andtrepresents time in seconds.a) Find the average rate of change of position between t = 0 and t = 1.b) Find the instantaneous rate att= a.c) Find the moment(s) when the particle is at rest.AROCSG56729 42o3567 43427RocIimSCathlscaleIrocin4a2h9hsohT2Cathfalath142949A41Roc4a9lim.yggqay.ygya.ggayqRocioatagoriaratechageof4990aat2.25seconds
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7. Evaluate:)*+# → 0√3</1√31/√9</1√91/t.im7iFEEIEi.FFiGtxFtxTIETEEIimyEx orzri tr2522Be
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8. Determine all values of the constants A and B so that the following functionis continuous for all values ofx.!(#) = GH# − I, *! # ≤ −12#9+ 3H# + I, *! − 1 < # ≤ 14, *! # > 17CA BIge243AxtBAB23AB2A2B2ABA Bf2x43AxtB544213AtB4213AtAB43BtstB23Bt 3tB24BIBa
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9. Find the value of the parameterasuch that the function f is continuous at any number :Ianlax2Case2A142a222a124a22aa
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10. Analyse the continuity of the functionourteafaCX72xt2TfCxJK12XczKzX21inflocC272xsI4t.intyaznotcontinuousat
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11. Solve the following limit:lim /→3# − √#√#=− 1LetxaaI16toEa2xatineaa4xaasga2ge1ina3aZagCaeCatesa3aka12limassCats1111242232
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12. Given that the slope of the tangent from the point (2,3) to the parabola!(#) = #9+ Ris2 , determine the value of “c”.--mentionca42ahth4caelimhSohhsnathlimhDh2Ame22a2afaItcPointoftanguyisC2,24Otherpoint213me9ok22tCf3I22436 41Cgofixx42
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13. Find the slope of the tangent line to the graph of the curve at the generic point(a, f(a)).mentiontGthfhng2cathltahh2atan.hntHtrn2arahfijn2hththhifz2rather1itatD21Tatra2t1Wa
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14. Consider the function . Determine the equation of the line perpendicular to the tangentof f(x) at point P (0,-1)FGC22221612fOth_fh2ht1_2hI2h12mIim22Hoh2K121244limhsohahghim4h so2hImImFyxtblasyIxs
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