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ƒCƒ‰ƒXƒg–³—¿ 4 ŒŽ ƒCƒ‰ƒXƒg ‚©‚í‚¢‚¢-Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historyYou can sign in to vote the answer Sign in Inggil 6 years ago GDP 0 0 Still have questions?

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I'll give you a hint to get you started If this doesn't help, either repost or email me (fg)(x) is shorthand notation for f(x)g(x) So (fg)(x) means that you add the functions f and gMonthly Subscription $499 USD per month until cancelled Annual Subscription $2999 USD per year until cancelled User Data Missing Please contact support We want your feedback (optional) (optional) Please add a message Message received Thanks for the feedback Cancel SendG X g 񋟂̌ ݗp t CAD f ^ E t C X g f ^ W B t @ C ` PNG EDXF EJWC EEXCEL ɑΉ Ă ܂ B g p 󋵂ɍ 킹 Ă I щ B ށE ݋@ B E S { ݁E ݍށE ܂ߐ} E ԁE l E i ρE ȂǁB ލ쐬 ɂ p B

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Links with this icon indicate that you are leaving the CDC website The Centers for Disease Control and Prevention (CDC) cannot attest to the accuracy of a nonfederal website Linking to a nonfederal website does not constitute an endorsement by CDC or any of its employees of the sponsors or the information and products presented on the website4 = −37 4 The number 3 4 is a representative of 3 4, but −37 4 is also a representative of 3 4 Indeed, any element of an equivalence class can be used to represent that equivalence class These ideas are summed up in Theorem 331 in Section 33 When we say several statements, such as P 1, P 2, and P 3 are equivalent, we mean P 14 S njn E Ɖu n E ċz n ̍\ ̑ ̓ ́A S njn E Ɖu n E ċz n ̍\ C X g ̃R s C g @ ۈ Õ w @

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(a) For any constant k and any number c, lim x→c k = k (b) For any number c, lim x→c x = c THEOREM 1 Let f D → R and let c be an accumulation point of D Then lim x→c f(x)=L if and only if for every sequence {sn} in D such that sn → c, sn 6=c for all n, f(sn) → L Proof Suppose that lim x→c f(x)=LLet {sn} be a sequence in D which converges toc, sn 6=c for all nLet >01)£ ÀÓšqí2‡ ‰NÏ×AÙ§¾Ä¶N ŸÏFiÏl¸5ìdiPT§è‡â‹ TÌY5šØ` Ç£s> ÑÖ¡Í«1ìb¨,c‰ä£ ç¹é Ŭ±‡ÚQ‹ÄÑ!½¤ÔöËTN¥ëdⳜ r ¹øÑ¥zà¸PÞ ê§³¬ù³ (T†zOž¼8ô±*ô­eÎÜE"ÈÞ žNî~=çE!òÀK¦8C ™"J mÎÒ ¤qOº ŽÔ²×ÇUžë–Ÿ âfy@z qâíÊ ¢F(Þ&Âe Hd Z°=½*WÃ(d) If f0 is continuous on −1,4, then Z 4 −1 f0(w)dw = f(4)−f(−1) This is true, since the antiderivative of f 0is f (that is, the derivative of f is f ) So, this is the Fundamental Theorem of Calculus, part II (e) Z 1 −2 1 x4 dx = − 3 8 False We cannot use the FTC on this integral since 1 x4 has a vertical asymptote at x = 0, which

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116 = H > B R G B D g Z F b g g h _ h e h ` d b y m g b \ _ j k b l _ l " K \ B \ Z g J b e k d b", L h f 53, K \I 1 1, F _ o Z g b a Z p b y, _ e _ d l j b n4 CHAPTER 1 RINGS AND IDEALS 15 We have the following (i) If f= P ∞ n=0 a nx n∈Ax is invertible, then obviously a 0 is a unit Conversely, if a 0 is a unit, then we may let b 0 be such that a 0b 0 = 1 and then we may define b n, n∈N recursively by the explicit relations they have to satisfy (ii) If f∈Ax is nilpotent, then so is aMonthly Subscription $499 USD per month until cancelled Annual Subscription $2999 USD per year until cancelled User Data Missing Please contact support We want your feedback (optional) (optional) Please add a message Message received Thanks for the feedback Cancel Send

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