HW03-solutions

HW03-solutions - husain(aih243 – HW03 – Gilbert...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: husain (aih243) – HW03 – Gilbert – (56215) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points Let F be the function defined by F ( x ) = x 2 − 25 | x − 5 | . (i) Determine lim x → 5 + F ( x ) . 1. limit = 5 2. limit does not exist 3. limit = − 5 4. limit = − 10 5. limit = 10 correct Explanation: After factorization, x 2 − 25 | x − 5 | = ( x + 5)( x − 5) | x − 5 | . But, for x > 5, | x − 5 | = x − 5 . Thus F ( x ) = x + 5 , x > 5 , in which case, by properties of limits, the right hand limit lim x → 5 + F ( x ) = 10 . 002 (part 2 of 3) 10.0 points (ii) Determine lim x → 5- F ( x ) . 1. limit = 10 2. limit = 5 3. limit does not exist 4. limit = − 10 correct 5. limit = − 5 Explanation: After factorization, x 2 − 25 | x − 5 | = ( x + 5)( x − 5) | x − 5 | . But, for x < 5, | x − 5 | = − ( x − 5) . Thus F ( x ) = − ( x + 5) , x < 5 , in which case, by properties of limits, the left hand limit lim x → 5- F ( x ) = − 10 . 003 (part 3 of 3) 10.0 points (iii) Use your results for parts (i) and (ii) to determine lim x → 5 F ( x ) . 1. limit = − 5 2. limit does not exist correct 3. limit = 5 4. limit = 10 5. limit = − 10 Explanation: By parts (i) and (ii), lim x → 5 + F ( x ) negationslash = lim x → 5- F ( x ) . husain (aih243) – HW03 – Gilbert – (56215) 2 Consequently, the two-sided limit does not exist . 004 10.0 points Determine the value of lim x → 2 4 f ( x ) g ( x ) 2 f ( x ) − 3 g ( x ) when lim x → 2 f ( x ) = 1 , lim x → 2 g ( x ) = − 4 . Correct answer: − 1 . 14286. Explanation: By properties of limits lim x → 2 4 f ( x ) g ( x ) = 4 lim x → 2 f ( x ) lim x → 2 g ( x ) = − 16 while lim x → 2 2 f ( x ) − 3 g ( x ) = 2 lim x → 2 f ( x ) − 3 lim x → 2 g ( x ) = 14 negationslash = 0 . By properties of limits again, therefore, lim x → 2 4 f ( x ) g ( x ) 2 f ( x ) − 3 g ( x ) = − 8 7 . 005 10.0 points Determine lim x → 2 braceleftBig 2 x 2 − 2 x − 1 x − 2 bracerightBig . 1. limit = 2 2. limit = 1 2 3. limit = − 1 3 4. limit = − 2 5. limit = 1 3 6. limit = − 1 2 correct 7. limit does not exist Explanation: After simplification we see that 2 x 2 − 2 x − 1 x − 2 = 2 − x x ( x − 2) = − 1 x for all x negationslash = 2. Thus limit = − lim x → 2 1 x = − 1 2 ....
View Full Document

{[ snackBarMessage ]}

Page1 / 9

HW03-solutions - husain(aih243 – HW03 – Gilbert...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online