final-practice - we„r QIfGP €‚eg„sgi psxev iˆewF the...

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Unformatted text preview: we„r QIfGP €‚eg„sgi psxev iˆewF the (rst two midterms —nd pr—™ti™e midterms —s — p—rt of the pr—™ti™e (n—lF €le—se noteX the —im of this pr—™ti™e (n—l is to give you sever—l pro˜lems on the m—teri—l not ™overed ˜y the (rst two midterms —nd pr—™ti™e midtermsF ‰ou should therefore tre—t IF vet f (x) = sin xF pind n so th—t „—ylor9s polynomi—l of degree n —round 0 —pproxim—tes sin(1) to within 10−2 F tustify your —nswerF PF vet f (x) = 2x + 4 . x3 − 1 f (x)dxF ixpress f (x) —s — sum of terms using p—rti—l fr—™tionsF …se this to ev—lu—te QF pind the „—ylor series for the fun™tion f (x) = ln(x − 1)F hetermine its r—dius —nd interv—l of ™onvergen™eF 1 RF pind the power series represent—tion of the fun™tion F hetermine its r—dius —nd 2 interv—l of ™onvergen™eF SF pind the limit of the sequen™e an = n1/n F TF ss the improper integr—l 0 ∞ (1 − x) sin(ex )dx ™onvergent or divergentc ixpl—inF UF pind the surf—™e —re— of the surf—™e of revolution o˜t—ined ˜y rot—ting the p—r—˜ol— y = x2 D 0 ≤ x ≤ 1D —˜out the y E—xisF VF …se the —r™length formul— to (nd the length of the ™ir™le of r—dius 1F WF hetermine whether the following series —re —˜solutely ™onvergentD ™ondition—lly ™onverE 1 1 gentD or divergentX @—A (−1)n n+sin(n) Y @˜A (−1)n n2 +sin(n) Y @™A e−n F I ...
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