Calculus 3 Problems;Homework


Calculus 3 Problems;Homework

Please handwrite all these problems. Please use a good black or blue ink thick enough for a camera or scanner to pick it up. Unless you have not able, we require that you write very neatly and from left to right.

Calculus 3  – papers homework that must be solved,Mathematical problems that you are required to solve them ( Homework 3 ).

  1. Problems Problems 1-8, no need to explain, just write down and hand in the correct choice. Other problems require some explanation. (1) Suppose that limx→∞ f(x) = ∞ and limx→∞ g(x) = −∞. Then always, (A) limx→∞ f(x) · g(x) = ∞ (B) limx→∞ f(x) · g(x) = −∞ (C) limx→∞ f(x) + g(x) = ∞ (D) limx→∞ f(x) g(x) = ∞

(2) Suppose that limx→∞ f(x) = ∞ and limx→∞ g(x) = 0. Then always, (A) limx→∞ f(x) · g(x) = ∞ (B) limx→∞ f(x) · g(x)=0 (C) limx→∞ f(x) − g(x) = ∞ (D) limx→∞ f(x) g(x) = ∞ .

(3) Suppose that limx→a f(x) = ∞. Then, (A) limx→a 1 f(x) = ∞ (B) limx→a 1 f(x) = 0 (C) limx→a 1 f(x) = −∞ (D) none of the above.

(4) Suppose that limx→∞ f(x) = 0 but f(x) > 0. Then, (A) limx→∞ 1 f(x) = ∞ (B) limx→∞ 1 f(x) = −∞ (C) limx→∞ 1 f(x) = 0 (D) limx→∞ 1 f(x) < 0.

(5) The function f(x) assumes only two values: 5 and 7. No matter how big N is, there is some x>N such that f(x) = 5 and there is some x>N such that f(x) = 7. We conclude that (A) limx→∞ f(x)=5 (B) limx→∞ f(x)=7 (C) limx→∞ f(x)=6 (D) limx→∞ f(x) does not exist.

(6) Let f(x) = 1 x2 . In order to ensure that f(x) > N, it is enough to require that (A) x>N (B) xN for some number N), the values of f(x) are closer to L = 3 than a number ε > 0.

(a) Sketch the graph y = 1 x + 3 and a horizontal strip such that 2.8 <y< 3.2=”” (if=”” you=”” are=”” using=”” the=”” grapher,=”” note=”” that=”” it=”” has=”” capability=”” to=”” display=”” more=”” than=”” one=”” graph=”” at=”” once.=”” functions=”” be=”” plotted=”” separated=”” by=”” a=”” semincolon;=”” can=”” input=”” 1=”” x+3;=”” 2.8;=”” for=”” this=”” problem).=”” based=”” on=”” decide=”” which=”” portion=”” of=”” y=”f(x)” is=”” contained=”” in=”” strip.=”” find=”” n=”” such=”” x=””>N the graph is included in the strip.

(b) For the following values of ε, using algebraic inequalities find N such that the graph y = 1 x + 3 restricted to x>N is contained in the horizontal strip 3 − ε

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