{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

K Final Exam-solutions

# K Final Exam-solutions - Version 096 – K Final Exam –...

This preview shows pages 1–4. Sign up to view the full content.

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

View Full Document

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

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

Unformatted text preview: Version 096 – K Final Exam – Hamrick – (54868) 1 This print-out should have 25 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Below is the graph of a function f . 2 4 6 − 2 − 4 − 6 2 4 6 8 − 2 − 4 Use the graph to determine lim x → 3 f ( x ) . 1. limit = 12 2. limit = 7 3. limit does not exist correct 4. limit = 4 5. limit = 3 Explanation: From the graph it is clear the f has a left hand limit at x = 3 which is equal to 3; and a right hand limit which is equal to 2. Since the two numbers do not coincide, the limit does not exist . 002 10.0 points Find the value of lim x → 3 2 x − 6 √ x − √ 3 if the limit exists. 1. limit = 6 √ 3 2. limit = 12 3. limit = 3 √ 3 4. limit does not exist 5. limit = 2 √ 3 6. limit = 4 √ 3 correct Explanation: Since x − 3 = ( √ x + √ 3)( √ x − √ 3) , we can rewrite the given expression as 2( √ x + √ 3)( √ x − √ 3) √ x − √ 3 = 2( √ x + √ 3) for x negationslash = 3. Thus lim x → 3 2 x − 6 √ x − √ 3 = 4 √ 3 . 003 10.0 points Determine lim x →∞ x 4 − 3 x 3 + 6 . 1. limit = 7 2. limit = 0 3. limit = ∞ correct 4. limit = −∞ 5. limit = 3 6. none of the other answers Explanation: 004 10.0 points Version 096 – K Final Exam – Hamrick – (54868) 2 Determine if lim x →∞ (ln x ) 2 6 x + 4 ln x exists, and if it does, find its value. 1. limit = ∞ 2. limit = 0 correct 3. limit = 10 4. none of the other answers 5. limit = 6 6. limit = −∞ Explanation: Set f ( x ) = (ln x ) 2 , g ( x ) = 6 x + 4 ln x . Then f, g have derivatives of all orders and lim x →∞ f ( x ) = ∞ , lim x →∞ g ( x ) = ∞ . Thus L’Hospital’s Rule applies: lim x →∞ f ( x ) g ( x ) = lim x →∞ f ′ ( x ) g ′ ( x ) . But f ′ ( x ) = 2 ln x x , g ′ ( x ) = 6 + 4 x , so lim x →∞ f ′ ( x ) g ′ ( x ) = lim x →∞ 2 ln x 6 x + 4 . We need to apply L’Hospital once again, for then lim x →∞ 2 ln x 6 x + 4 = lim x →∞ 2 x 6 = 0 . Consequently, the limit exists and lim x →∞ (ln x ) 2 6 x + 4 ln x = 0 . 005 10.0 points Determine lim x → 4 x tan − 1 (5 x ) . 1. limit = 4 5 correct 2. limit = 0 3. limit = 4 4. limit = 5 4 5. limit = 1 5 6. limit does not exist Explanation: Since the limit has the form lim x → 4 x tan − 1 (5 x ) = , we use L’Hospital’s Rule with f ( x ) = 4 x, g ( x ) = tan − 1 (5 x ) . For then lim x → f ( x ) g ( x ) = lim x → f ′ ( x ) g ′ ( x ) = lim x → 4(1 + (5 x ) 2 ) 5 . Consequently, limit = 4 5 . 006 10.0 points Determine which (if any) of the following functions is not continuous at x = 5. 1. all continuous at x = 5 Version 096 – K Final Exam – Hamrick – (54868) 3 2. f ( x ) = braceleftbigg | x − 5 | x negationslash = 5 x = 5 3. f ( x ) = braceleftBigg 10 2 x − 5 x negationslash = 5 2 x = 5 4. f ( x ) = braceleftBigg 1 x − 5 x negationslash = 5 5 x = 5 correct 5. f ( x ) =...
View Full Document

{[ snackBarMessage ]}

### Page1 / 12

K Final Exam-solutions - Version 096 – K Final Exam –...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online