Math 1210, Comprehensive Review 1. Define what is meant by each of the following: a) lim x → c f ( x ) = L b) lim x → c f ( x ) = ∞ c) lim x →∞ f ( x ) = L d) lim x →∞ f ( x ) = ∞ 2. Find each of the following limits. Show all work. a) lim x→ 3 x 2 + x − 12 x − 3 b) lim x→ 4 2 − x 4 − x
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Math 1210, Comprehensive Review - Utah State University
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3.Definewhatitmeansforafunctionftobecontinuousat x = a .4.Whatcanyousayaboutthefunctionfwhosegraphisgivenbelow?
5.a)Definecarefully,intermsofalimit,thederivativeofafunctionfatthepoint x = x0 .Itisdenotedby f '(x0 ) .b)Whatarethetwoimportantinterpretationsof f '(x0 ) ?c)Let y = f (x) = x2 +1 .Usethedefinitionofthederivativetofind f '(1) .
9.Let f (x) = x3 + 7 .Findthederivativeof f −1 at x = 8 . 10.Let y = ( sin x )x .Find y ' .11.Twocommercialplanesareflyingatanaltitudeof40,000feetalongstraight-linecoursesthatintersectatrightangles.PlaneAisapproachingtheintersectionpointataspeedof442knots.PlaneBisapproachingtheintersectionat481knots.AtwhatrateisthedistancebetweentheplaneschangingwhenplaneAis5nauticalmilesfromtheintersectionpointandplaneBis12nauticalmilesfromtheintersectionpoint?
12.Findtheabsolutemaximumandminimumofthefunctiondefinedby f (x) = 4 − x3 on [−2 ,1 ] .13.Let f (x) = 2x3 − 6x +1.Identifytheintervalsonwhichfisincreasingordecreasing.Findthelocalandabsoluteextremevalues.Determinewherefisconcaveupandwhereitisconcavedown.Findallpointsofinflection.