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Limits -solutions-1

# Limits -solutions-1 - handa(nh5757 – Limits –...

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Unformatted text preview: handa (nh5757) – Limits – bormashenko – (54880) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points Which of the following statements are true for all values of c ? I. lim x → c f ( x ) = 0 = ⇒ lim x → c | f ( x ) | = 0 . II. lim x → c | f ( x ) | = 0 = ⇒ lim x → c f ( x ) = 0 . 1. Both I and II correct 2. Neither I nor II 3. I only 4. II only Explanation: If f ( x ) is close to 0, then | f ( x ) | also must be close to 0. Conversely, if | f ( x ) | is close to 0, f ( x ) must also be close to 0. Therefore Both I and II are true . 002 (part 2 of 2) 10.0 points Which of the following statements are true for all c and all L ? I. lim x → c f ( x ) = L = ⇒ lim x → c | f ( x ) | = | L | . II. lim x → c | f ( x ) | = | L | = ⇒ lim x → c f ( x ) = L. 1. II only 2. I only correct 3. Neither I nor II 4. Both I and II Explanation: If f ( x ) is close to L , then | f ( x ) | must be close to | L | no matter what the value of L is. So I is true. But II not true for all L and c . To see that, let f ( x ) = x , c = − 2 and L = 2. Then lim x → c | f ( x ) | = lim x →- 2 | x | = 2 = | L | . On the other hand, lim x → c f ( x ) = lim x →- 2 x = − 2 negationslash = L. Consequently, Only I is true . 003 10.0 points Below is the graph of a function f . 2 4 − 2 − 4 2 4 − 2 − 4 Use the graph to determine lim x → 2 f ( x ). 1. limit = 0 2. limit = 1 3. does not exist 4. limit = − 2 correct 5. limit = − 1 Explanation: handa (nh5757) – Limits – bormashenko – (54880) 2 From the graph it is clear that the limit lim x → 2- f ( x ) = − 2 , from the left and the limit lim x → 2+ f ( x ) = − 2 , from the right exist and coincide in value. Thus the two-sided limit exists and lim x → 2 f ( x ) = − 2 . 004 10.0 points Suppose lim x → 5 f ( x ) = 4 ....
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Limits -solutions-1 - handa(nh5757 – Limits –...

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