calc1 - pokharel (yp624) HW01 Radin (56520) This print-out...

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pokharel (yp624) – HW01 – Radin – (56520) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Express the number r = 3 2 + 1 1 + 1 3 in its simplest Form. 1. r = 3 4 2. r = 9 3. r = 9 2 4. r = 9 4 correct 5. r = 3 2 6. r = 3 Explanation: Since 1 + 1 3 = 4 3 , we see that r = 3 2 + 3 4 = 12 + 6 8 = 9 4 . keywords: 002 10.0 points SimpliFy the expression p 3 x 2 z 2 x 3 y 2 P 3 as much as possible, leaving no negative ex- ponents. 1. x 3 3 z 3 y 3 2. x 15 y 6 27 z 6 correct 3. x 3 z 2 y 2 4. x 15 27 z 6 5. x 15 27 z 6 y 6 Explanation: By the Laws oF Exponents, p 3 x 2 z 2 x 3 y 2 P 3 = p 3 z 2 x 3+2 y 2 P 3 = 3 3 z 2 · 3 x 5 · 3 y 2 · 3 which aFter simplifcation becomes x 15 y 6 27 z 6 . keywords: 003 10.0 points Which, iF any, oF the Following statements are true when a, b are real numbers? A. For all positive a and b , a + b = r a + 2 ab + b. B. For all positive a and b , a b a + b = a b. C. For all a and b , r ( a + b ) 2 = a + b . 1. A only 2. none oF them
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pokharel (yp624) – HW01 – Radin – (56520) 2 3. A and B only correct 4. B and C only 5. C only 6. B only 7. all of them 8. A and C only Explanation: A. TRUE: by the known product, ( x + y ) 2 = x 2 + 2 xy + y 2 . On the other hand, r ( x + y ) 2 = | x + y | , so if x + y > 0, x + y = R x 2 + 2 xy + y 2 . But if a, b are positive we can set x = a and y = b . The result follows since x and y are then positive. B. TRUE: by the known diFerence of squares factorizaation, x 2 y 2 = ( x y )( x + y ) . But if a, b are positive we can set x = a and y = b . The result follows after division. C. ±ALSE: r ( x + y ) 2 = | x + y | , and since R ( · ) is always non-negative, the right hand side has to be non-negative. But if a, b can be positive or negative, an absolute value sign is then needed on the right. keywords: square root, properties of square root, PlaceUT, True±alse, T/±, 004 10.0 points ±ind the domain and range of the function h ( x ) = R 9 x 2 . 1. domain = [0 , 3] , range = [3 , 3) 2. domain = [ 3 , 3] , range = [0 , 3] cor- rect 3. domain = [0 , 3] , range = [0 , 3] 4. domain = ( 3 , 3) , range = (0 , 3) 5. domain = [ 3 , 3] , range = [ 3 , 3] 6. domain = ( −∞ , ) , range = [0 , ) Explanation: If we write y = R 9 x 2 , then x 2 + y 2 = 9 whose graph is a circle centered at the origin having radius 3. Thus the graph of h is the upper semi-circle shown in 3 3 3 Consequently, h has domain = [ 3 , 3] , range = [0 , 3] . keywords: range, range of function, circle, domain, domain of function, 005 10.0 points There is a linear relationship T F = mT C + b between the temperature T F on the ±ahren- heit scale and its equivalent T C on the Centi- grade scale. As the thermometers
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pokharel (yp624) – HW01 – Radin – (56520) 3 32 212 0 100
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calc1 - pokharel (yp624) HW01 Radin (56520) This print-out...

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