Limits -solutions-2

# Limits -solutions-2 - handa(nh5757 Limits bormashenko(54880...

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handa (nh5757) – Limits – bormashenko – (54880) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – fnd 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. Io n l y 4. II only Explanation: IF f ( x )isc loseto0 ,then | f ( x ) | also must be close to 0. Conversely, iF | f ( x ) | is close to 0, f ( x )mustalsobecloseto0.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. n l y correct 3. Neither I nor II 4. Both I and II Explanation: IF f ( x )i sc lo seto L ,th en | 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 .Toseetha t , let f ( x x , c = - 2and L =2.Then lim x c | f ( x ) | =l i m x →- 2 | x | =2= | L | . On the other hand, lim x c f ( x )= l im x 2 x = - 2 ± = L. Consequently, Only I is true . 003 10.0 points Below is the graph oF a Function f . 24 - 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:

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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 . Which of the following statements are true without further restrictions on f ?
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Limits -solutions-2 - handa(nh5757 Limits bormashenko(54880...

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