# A p 9 0 b p 0 7 c p 5 3 5 d p 4 4 e p 6 2 6 2 f p 2 2

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(a)P(9,0)(b)P(0,-7)(c)P(53,-5)(d)P(-4,4)(e)P(-62,-62)(f)P(2,23)14. Sketch the graph of the given polar equation.(a)r= 2 sin 3θ(b)r= 2-4 cosθ(c)r= 2 + sinθ 15. Convert the given equation from polar to cartesian coordinates.What is the graph of theequation (name the curve)? 16. Convert the given equation from cartesian to polar coordinates. 17. Find the area enclosed by the curver= 8 sin 4θfromθ= 0 toθ=π4.18. Find the area enclosed by the curver= 8(1 + sin 2θ) fromθ=-π4toθ=3π4.19. Find the area enclosed by the closed curver= 2-2 cosθ.20. Find the area of the region lying outside the circler= 2 but inside the circler= 4 sinθ.21. Find the area of the region lying outside the curver= 2+sinθbut inside the curver= 5 sinθ.22. Find the area of the region that lies outside the curver= 2 sin 2θbut inside the curver= 3.(See the graph.) – 14–
MATH-2212: Calculus of One Variable IIStudy Guide for Final Exam, Fall 201923. Find the area of the region that lies outside the curver= 1 + cosθbut inside the curver= 3-sinθ.(See the graph.) 24. List the first five terms of the sequence defined by the given formula. Assume that indexing starts fromn= 1.(a)an= 3 + (-1)n·n2(b)an=n! + 1(n+ 1)!(c)a1= 7, andan+1= 5an-3 25. For the given sequence (an): find its limit or show that it doesn’t exist, determine whetherthe sequence is bounded, and determine whether it is monotonic. 26. Find the limit of the given sequence (or prove that it diverges). (a)lim(b)lim(c)lim(d)lim(e)lim(f)lim(g)lim(h)limn→∞n2-3n+ 412n2-4n+ 15n→∞n2-3n+ 412n3-4n+ 15n→∞n3-3n+ 412n2-4n+ 15n→∞3n2+ 2n-42n4+n-5n→∞4n2+nnn→∞n1 +nn→∞cosπn22n2+n+ 1n→∞lnn2+n+ 1n2-n+ 1(i)limn→∞arctan1-2n21 + 2n(j)limn→∞n+ (-1)nn(k)limn→∞(3 + 0.6n)(l)limn→∞(1.4n+ 0.6n)(m)limn→∞2 +3n+24n-2(n)limn→∞23n7n+2 – 15–
MATH-2212: Calculus of One Variable IIStudy Guide for Final Exam, Fall 2019(o)limn→∞lnn2n(p)limn→∞1 +6nn/2(q)limn→∞1-1n4n(r)limn→∞3100nn!Answers to Practice Problems1.(a)π4(b)-32(c) Diverges(d) Diverges(e)53·43/5(f) Diverges(g) 1(h) Diverges(i) Diverges(j)18(k) Diverges(l) Diverges2.(a) ln(3 + 22)(b)24827(c)496(d) 2(55-1)(e)π2(f)π28(g) 6π(h)174(e8π-1)3.(a)x= 2y2+ 4y-3; the graph is:(b)y= 2x+ 1 for-1x3; the graph is:(c)(x-1)24+(y+ 2)29= 1; the graph is:– 16–
MATH-2212: Calculus of One Variable IIStudy Guide for Final Exam, Fall 2019(d)y=34x2-1; the graph is:(e)y= sinπx2; the graph is:(f)y=32x+12forx >1; the graph is:4.
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